Combine the first 2 ingredients in a small bowl to make the Seasoning Mix.
Trim any remaining bits of skin from the tilapia fillets. Rub the fillets lightly on both sides with 2 teaspoons of the vegetable oil, and sprinkle one side of the fillets with 2 teaspoons of the seasoning mix.
Place a 14-inch nonstick skillet over high heat until the pan is very hot, about 4 minutes. Place the fillets in the pan, seasoned side down. Sprinkle the remaining sides evenly with 2 teaspoons of the seasoning mix.
Cook, turning once, until the fillets are just cooked through, about 2 to 3 minutes per side. The fish is cooked when the flesh flakes away easily. Transfer the fillets to a large plate and with a fork gently break the meat into bite-size pieces. Set aside.Place a 5-quart pot over high heat and add the remaining 2 tablespoons of vegetable oil and 2 tablespoons of the butter. When the butter melts and sizzles, add 1 cup of the onions, 1 cup of the celery, the parsnips, and the remaining Seasoning Mix. Cover and cook, uncovering every 2 minutes to stir, for 10 minutes, then uncover and stir in the flour until the white is no longer visible. If the mixture sticks hard on the bottom, add a little stock and scrape to loosen it. Add the remaining 1 tablespoon of butter and stir until the butter melts and is incorporated. Cover and cook until the vegetables stick hard to the bottom of the pot, about 4 minutes. Stir and scrape the bottom of the pot, then add 4 cups of stock and scrape until all the brown bits are loosened from the bottom of the pot. Re‑cover and cook for 8 minutes. At this stage, the front flavor is moderately salty, with light flavors from the flour underneath. The middle taste is the bell pepper flavor, sweetness from the parsnips, and the light herb and spice flavors which linger into the final taste. Add the mushrooms, all the bell peppers, and the remaining onions and celery. Stir well and continue to cook until the mixture boils rapidly, about 6 to 8 minutes.
Reduce the heat to medium, then stir and re-cover the pot. Continue to cook for 6 more minutes, then add the reserved fish. When you taste the soup, you'll notice that the sweetness has moved forward to become a front flavor, now salty-sweet, followed immediately by a roux and vegetable flavor and a rapid build and fading of the seasonings. Also note the underlying taste of the seafood or shrimp stock which binds all the other tastes together. At this point check the liquid - - here's where you add more stock if necessary to obtain a good "soup" consistency. Increase the heat to high, bring the liquid to a full boil and cook for 1 more minute. Remove from the heat and serve immediately.