Sauté the aromatics. Melt the butter in a large skillet over medium heat. Add the green bell pepper, onion, celery, and garlic and cook until the vegetables become tender, stirring occasionally, about 5 minutes.
Bloom the spices and cook the flour. Stir in the Cajun seasoning and cook for 1 minute for the spices to bloom and become fragrant. Sprinkle with the flour and cook for 1-2 minutes so the flour loses its raw flavor.
Simmer to thicken. Stir in the chicken broth (or water or shrimp stock), then the diced tomatoes, thyme, bay leaf, kosher salt, black pepper, cayenne pepper, and hot sauce. Bring to a simmer then reduce to low and cook for 20-25 minutes or until thickened, stirring occasionally. Add more broth or water as needed.
Cook the shrimp. Add the shrimp and cook just until opaque and cooked through, about 5 minutes. Add more broth or water if the broth is too thick.
Garnish and serve. Taste for seasoning then sprinkle with green onion and chopped parsley, and serve over white or brown rice.
Notes
To store: Leftovers will keep stored in the refrigerator for up to 3 days. Reheat over the stove (not in the microwave or the shrimp could get overcooked and tough), over low heat. If the sauce is too thick, add a bit of broth to the pan.