You could easily leave out all the meat, increase the overall amount of vegetables and make this vegetarian or even vegan if you omit the butter as well. I can't think of any vegetables to use to substitute for the meat that wouldn't greatly change the dish, but some fake sausage (blech!) may not hurt.
But I eat meat, so we'll start with the chicken. You can cut it into serving pieces or just quarter it. I like to pull the skin off now because it's going to get tossed anyway. This also reduces the amount of chicken fat that ends up in the final dish. Rub you chicken with a mixture of
1 tsp paprika
1 tsp thyme, dry
1/2 tsp basil, dry
1/2 tsp salt
1/2 tsp pepper
1/4 tsp ground red pepper
Dredge the chicken in about 1 cup of flour. Heat a pan on the stove with some olive oil, about medium high, brown it well on both sides. As the chicken is about ready to remove, turn the heat down to a little below medium. You're going to make a roux next and you don't want the pan too hot or the bottom will burn.
A roux is just a mixture of fat and flour. You will want about a 3 Tbs of each. If there is that much fat in the pan, use it. I use a combination of olive oil and butter. Omitting the butter is fine if you want to use olive oil. Keep the heat low enough so that this doesn't burn. You do want it to cook until it's nice and dark brown which could take up to 20 minutes. Note that most cooking that involves a roux will NOT require that you cook it nearly this dark.
As the roux starts to get really dark, add
1 onion diced
1 red pepper diced
1/2 green pepper diced
1/2 cup celery diced
1/2 cup sausage diced
I usually use kielbasa as at's always easy to find. The JoC also suggests smoked ham
cook till the vegetables are a little soft and add
I use 3-5 cloves depending on size because I like a lot of garlic. 2-3 would be more normal.
1/4 tsp thyme
1/4 tsp sage, crumbled
after about a minute add
2 cups liquid
You can use water, but . . .JoC calls for chicken stock. I've used vegetable stock as well as half vegetable stock and half chicken stock. You could use beer. You could use 1/4 to 1/2 cup of wine and some water.
3 Tbs tomato paste
1 Tbs worcestershire sauce
hot sauce to taste
Bring this to a boil and turn heat down to a simmer. Return the chicken to the pan and cover pan with lid. Let it simmer for 20-30 minutes, until the chicken is cooked through. Remove the chicken when it finishes cooking. If the sauce is too thick, turn the heat up and reduce it till it's where you want it. Don't thicken it too much as it will thicken as it sits, and it will be especially thick as leftovers the next day. It shouldn't need to much thickening.
Serve over steamed rice. I learned personally that if I pick the chicken, it's a shit ton easier to reheat as leftovers. Reheating chicken on the bone is a pain in the ass. I prefer not to mix the chicken back into the sauce because, if it's cooked well, the chicken with the spice mix cooked onto it really fucking rocks.