For the Seasoning Mix: Combine the seasoning mix ingredients in a small bowl.
For the Chicken with Tasso: Sprinkle the chicken pieces with 2 tablespoons of the seasoning mix and rub well with your hands. In a heavy 4-quart pot, preferably nonstick, heat the olive oil over high heat until it begins to smoke, about 3 to 4 minutes. Add the chicken, in batches if necessary, skin sides down first, and large pieces first, and cook until the skin is brown, about 4 minutes. Turn the pieces over and cook just until the other sides are brown but the chicken is not cooked through, about 4 minutes. Remove the chicken from the pot and set aside. To the same pot add the onions, celery, peppers and all the tasso. Stir well and scrape the bottom of the pot loosen the brown bits left from the chicken. Continue to cook, stirring frequently, for 3 minutes-the colors are so bright they're almost glowing-then add the remaining seasoning mix and the garlic. Stir well, then cover and cook for 5 minutes. Uncover and stir well, you'll see that the vegetables are beginning to brown and stick slightly. Scrape the bottom of the pot to loosen any sticking material, then re-cover and cook for 4 minutes. At this point the vegetables are medium brown and may be sticking hard, so add 1/2 cup of stock and deglaze the pot by scraping to loosen all the material on the bottom. Add the flour and stir until the white is no longer visible, adding a little more stock if necessary to help absorb the flour. Scrape the bottom of the pot one more time, then cover and let the mixture cook for 3 minutes. Warning: do not do this if your pot does not have a good thick bottom. A thin pot will heat too quickly and your mixture will definitely burn, so reduce the heat and watch closely to be sure that the food doesn't burn. Your cooking time may have to be a little longer to make up for using less heat. But if you do have a good heavy bottomed pot, you'll discover that flour moistened with the juices from the vegetables and tasso creates a wonderful flavor when it is allowed to brown in this way. Uncover, add the remaining 2 1/2 cups of stock, and scrape the bottom of the pot well. Bring to a boil, return the chicken and any accumulated juices to the pot, and return the liquid just to a boil. At this time, the broth is reminiscent of gumbo, but very salty from the seasonings. Reduce the heat to medium, recover and cook, stirring and scraping the pot occasionally, until the chicken is fully cooked, about 25 minutes. Serve over rice.
Recipe courtesy of "Chef Paul Prudhomme's Louisiana Tastes: Exciting Flavors from the State that Cooks" by Paul Prudhomme