In a heavy-bottomed pot over medium-low heat, melt the butter and whisk in the flour to create a roux, cooking for 30-40 minutes until deep chocolate brown.

Add the diced celery, yellow onion, green bell pepper, and minced garlic to the roux. Sauté for 8-12 minutes until softened.

Slowly whisk in the beef broth, bring to a gentle boil, and let it simmer for 15-20 minutes.

Stir in the sliced andouille sausage, stewed tomatoes, tomato sauce, hot sauce, white sugar, Cajun seasoning, dried thyme, and bay leaves. Simmer uncovered for about 45 minutes.

Add the medium shrimp and Worcestershire sauce, sprinkle in the gumbo filé powder, and cook on low heat for an additional 45-60 minutes.

Just before serving, stir in an additional teaspoon of gumbo filé powder and ladle over cooked white rice.