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.
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.
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.
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. Taste for seasoning then sprinkle with green onion and chopped parsley, and serve over white or brown rice.