Before we start, I just want to say that I'm a firm believer in the credo that there's no perfectly-right way to make Cajun food. There are plenty of WRONG ways, but the beauty of cajun is it's background ... whatever was available can be put into a gumbo. That's why a seafood gumbo sometimes has more pescatarian ingredients than a local aquarium. It's all good. Get the basics right, and then experiment and make it your own. Donald Link (Cochon, Herbsaint) tells stories of growing up in Acadian parish, where Gumbo was the sunday meal, and it contained whatever the family hadn't finished throughout the week. That's the gumbo I make. There are lots and lots and lots of very qualified coonasses on this site; we can all learn from every one of them. Pescado and Brisket lead the way, btw.
My family is cajun several generations back. My aunts still have a working understanding of spoken french, even though they can't write or read a lick - comes from listening to my grandmother, and great-grandmother shout at each other. When I was old enough to care about such things, my family put together a cookbook for me, and the family gumbo recipe was inside. When I need a chuckle, I'll go read it again. There's not a single ingredient that has an explicit portion listed. The recipe calls for "a medium onion" and "some salt" (and so on). One of my aunts loves the fact that she literally had to stand next to my grandmother and watch her make it, so she could write it down for me. Ours is a simple recipe, made even simpler by my current brood that are a little bit spice-averse. You won't find jalapenos in mine, or poblanos, or even white pepper; all of these 100% belong in a gumbo if you want them. We also don't use Okra, and I don't want to get into a holy war here. We're a file family, but it don't make a shit; eat what you like.
Needed ingredients, chicken and sausage gumbo:
10 cups chicken stock (see below for some detail on this ... )
Chick from 8 chicken thighs, de-boned and lightly shredded
Two links sausage of your choice (if it were just me, this would be a good spicy cajun andouille ... but my family requests a less-spicy option, usually. It don't matter - eat what you like), sliced into rounds
Medium onion, slightly smaller than your fist, diced.
Medium-sized bell pepper (traditionally it's a green one, but again, use what you like), diced.
Four stalks of celery (give or take), chopped
Four cloves of garlic (give or take), minced.
1/2 cup flour
1/2 extra virgin olive oil
salt and fresh ground black pepper (to taste)
A note on the oil; some/many recipes will call for good ole' vegetable oil, but modern medical science looks poorly on the 'expressed' oils. I've made this with both, and 100% cannot tell the difference. If you use oil for your roux (which I do), use good olive oil. If you prefer something like duck fat, bacon grease, etc, that's awesome too. Eat what you like.
First, you make a roux. Actually, not quite. I find one of the key controls of flavor in the finished product is the quality of the stock used. And since you need to pre-cook the chicken anyway, let's make the stock ourselves. The ingredients here aren't in the list above.
Fill a stock pot with 12-14 cups of water
Rough-chop an onion, three raw carrots, a few sticks of celery, and put in the pot
Liberally season with salt, pepper. Don't tell anyone, but a good dash of Italian Seasoning here adds some savory that I quite like. Throw in a bay leaf too.
Bring to a boil, add chicken thighs
Here's the magic ... when the chicken is done, debone it and return the bones to the stock.
Reduce heat and simmer stock, bones and veggies until stock reduces by about 25%. You want a nice, oily look.
Strain veggies and bones, set stock aside. You're looking for about 10 cups, but if you end up with fewer that's ok because you're just concentrating the flavor even more. Add store-bought stock when making gumbo, if you have to.
Onto the main course!
Now, you make a roux. Get yourself a good flat-bottomed dutch oven, or some other equally heavy-duty flat-bottomed pot.
Add flour and oil to the pot, with your stove on low heat. Use a whisk to combine them.
Low heat. Lower. Trust me. Lower. That's better.
You'll read "stir constantly" in most recipes you'll find for making a roux. It's necessary in the later stages, but not early on. Give it a few minutes, then stir. The mixture will start to bubble; when it does, stir. As the roux cooks, you'll end up stirring more often, and for the last half of the cook time, you'll be stirring basically constantly. You'll get a feel for it - the first few times you do it, stir a lot. Once you know what to expect, you can back off on the early stages.
The key to making a tasty roux is color. You want the roux to be dark brown.
If you've ever made hot chocolate by melting dark chocolate in a double-broiler, then you've seen both the consistency and color that your final roux should hit.
If you've never done hot chocolate that way, what's wrong with you? Do it now; it's AMAZING.
If you still need a color reference, cook until the roux looks like the color of the outside of an old mahogany grandfather clock. "Paper grocery bag" is way too light. "Old copper penny" is getting closer, and would make a fine gumbo if you so chose, but you can go darker.
If the roux starts to flake off the bottom of the pan and the dark pieces don't re-integrate with the rest of the roux, or if your house starts to smell like burned ass, you burned the roux. Welcome to the club, everyone does it. Throw it out (CAREFUL - that shit is hot), and start over. No harm, no foul.
When the roux is done, immediately add all the veggies.
This has the effect of stopping the roux cooking process. It'll throw off a great saute smell. Aside from the eating, this is my favorite part of the process.
Saute veggies in the roux for 6-8 minutes, until the celery is soft but not mushy.
Note - prior to this step, make sure your chicken stock is warm. If you've made the stock directly before making the gumbo, then it's probably still warm. If it's not warm for whatever reason, warm it up. Low heat in another pot while you make the roux works well.
Add 2-3 cups of warm stock to the roux, and stir to incorporate.
The roux may separate slightly due to temperature mismatches, but should recombine in short order.
Add remaining stock.
Add chicken and sausage.
Salt and pepper to taste.
Remember that the sausage will add salt, so don't overdo it. Your guests can always add more
Pepper is strong, esp if you have time to let the gumbo simmer for a while. Don't go crazy.
Add another bay leaf.
Simmer for ... a while. An hour at least. Two is better. Three is even better.
Make white rice. Buy gumbo file and crystal hot sauce. Put a serving of rice in a bowl, cover liberally with gumbo, making sure to get plenty of chicken and sausage in there. Top lightly with file, and hot sauce to taste.
Cold beer and a spoon, and you're off to the races.
IF you're in the mood for something more adventurous, I recommend Donald Link's recipe here https://www.saveur.com/article/recipes/fried-chicken-and-andouille-gumbo/.