I've been making this recipe for years, it's one of a prized handful that I have soaked into my bones and can make by memory and intuition now. Honestly, I don't have a hard-and-fast origin for it...I'm sure some aspects were cribbed from tips on Chowhound threads, perhaps others from Paul Prudhomme, but it has since evolved into something more or less my own. Now it's yours, too.
Chicken, Shrimp and Andouille Gumbo
*1-2 lbs bone-in, skin-on chicken parts (thighs are my go-to parts), trimmed of excess fat
*4 cups chicken stock
*1 1/2 cups water
*5 bay leaves
*1 generous tablespoon of Cajun seasoning. I highly recommend making your own; store bought just doesn't cut it. I loosely follow Emeril's Essence recipe, which is great. I lessen the salt and the thyme somewhat and add a smidge of home ground mulatto chile powder.
*1/2 cup fat (in order of personal preference - duck fat, bacon fat, neutral oil, butter. Butter burns the easiest, but sure is tasty. Use what you will.)
*1/2 cup flour
*'Holy trinity' - one cup each of diced yellow onion, celery, green bell pepper. Try for a dice that doesn't exceed 1/2in.
*3-4 minced cloves of garlic
*Half a small can of diced tomatoes, partially drained
*Tabasco hot sauce
*Healthy pinches of dried thyme, oregano, paprika, red pepper flakes, cayenne, salt & pepper
*2-3 andouille sausage links
*1/3-1/2 lb shrimp
Bring a large pot of water to a boil, add the chicken, and boil for a minute or two before draining and rinsing the chicken off - this step removes some impurities from the chicken. Rinse the pot out and add the stock, water, bay leaves and seasoning, along with a sprinkling of salt, and bring to a boil. Add the chicken back to the pot, reduce the heat to medium-low, and poach for 25-30 minutes until the chicken is just cooked through.
Remove the pieces and set aside; strain & skim fat from 4 cups of cooking liquid to reserve for the gumbo. Once the chicken is cool enough to handle, loosely shred chicken meat, tossing the skin and bones. I recommend using the oh, cuppish or so of leftover cooking liquid to supplement the water for the rice - gives the rice an added boost of flavor. I also usually make a side of macque choux, which uses some up, too.
Make the roux- heat your fat in a large dutch oven or heavy-bottomed pot over medium-high to high heat, and when it gets hot sprinkle in the flour, whisking constantly. Continue to whisk thoroughly and constantly - and quickly! until roux cooks to a deep reddish-brown color. No lighter than the caramel color of peanut butter allowed - I usually go for the color of milk chocolate but have been known to call it quits a little before that if my hands are screaming at me. The time this takes really depends on how high you’re comfortable with placing the heat. I usually whisk for about 15 minutes at medium-high heat before the darkening starts to quicken, and then a couple minutes more until it's at the desired level of doneness, but if you set the heat to a comfortable medium, you might be whisking for 30+ minutes. Feel free to modulate the temperature if that makes it easier. If you see black specks, the roux is burnt and you’ll need to throw it out and try, try again. Don't go burning yourself whilst whipping up a maelstrom in the roux; it is as hot as its nickname, 'cajun napalm', would suggest.
Remove the pot from the heat once the roux looks right and immediately stir in the trinity and minced garlic. A grand sizzle will resound as applause for a roux well done. Return pot to medium-low heat and cook, stirring frequently, until vegetables are starting to soften, about 4-5 mins. Slowwwwwly stir in the reserved 4 cups of chicken liquid and the diced tomatoes, making sure to adequately blend the mixture after each liquid addition. Add two bay leaves, a couple shakes a'piece of dried thyme and oregano, a scant half-teaspoon of cayenne (or whatever you’re comfortable with, heat-wise), a few healthy dashes of Tabasco, salt & pepper, a few shakes of red pepper flakes, a good dash or two of paprika, a spangling of Cajun seasoning and a pinch of sugar. All of this is to personal taste, so adjust accordingly. Turn heat to high and bring to a boil. Immediately after it boils bring the heat down and simmer for at least an hour, or indefinitely. I usually let it go for about 2, but I've sometimes transferred it to a crock pot after that point and kept it on low for half a day.
Meanwhile, brown one or two bias-sliced andouille links or other sausage of your choice (andouille is best, of course) in a pan and then add to the gumbo along with reserved chicken about 30-45 mins into its simmer. A few minutes before soup's on, throw the shelled, deveined shrimp in the gumbo pot until they are just cooked through. Fish out the bay leaves and then ladle the gumbo over rice and garnish with some chopped scallions or parsley if you'd like some green.