In the Dutch oven, melt the butter with 1 tablespoon of the canola oil over medium heat. Add the brown rice flour and whisk until the flour turns golden brown and has a nutty taste, about 10 minutes. Transfer the flour mixture to a bowl and set aside.
Heat the remaining canola oil in the Dutch oven and add the onions, celery, peppers, and garlic. Sauté until they are softened, about 3 to 5 minutes. Return the flour mixture to the pot.
Add the tomatoes, tomato sauce, thyme, bay leaf, black pepper, red pepper flakes, hot sauce, brown sugar, and chicken stock. Stir and bring it all to a boil. Reduce heat and cook covered at a simmer for about 30 to 40 minutes. Season with salt and cayenne pepper to taste, then remove the bay leaf.
Add the shrimp and cook until just pink, about 2 to 3 minutes. Serve immediately in bowls over rice, and garnish with the chopped parsley.