Make the Roux: In a large Dutch oven, heat butter or oil over medium heat. Whisk in flour to form a paste. Stir constantly for 20–30 minutes until the roux turns a dark brown color.
Add Vegetables and Sausage: Stir in the chopped onions, celery, and bell pepper. Add the sliced andouille sausage and cook for 5–7 minutes until the vegetables soften and the sausage browns slightly.
Add Broth and Seasonings: Pour in the chicken or seafood broth. Add Cajun seasoning, paprika, thyme, bay leaves, cayenne pepper, salt, and pepper. Stir well and bring to a boil.
Simmer: Reduce the heat to low and let the gumbo simmer for 45 minutes to 2 hours. The longer it simmers, the richer the flavor.
Add Shrimp and Thicken: In the last 10–15 minutes of cooking, add the shrimp. If using okra or file powder, add them now to thicken the gumbo.
Adjust Seasoning and Serve: Taste and adjust seasoning as needed. Remove from heat and let the gumbo sit for 5–10 minutes. Garnish with fresh parsley or green onions. Serve hot over white rice.