In a large 6-quart pot over medium-low heat, melt ¾ cup of unsalted butter. Gradually whisk in 1 cup of all-purpose flour until smooth. Continue whisking constantly for 30-40 minutes until the roux reaches a deep, rich brown color, resembling chocolate.

While the roux cools, chop 2 ribs of celery, 1 large onion, 1 large green bell pepper, and mince 2 teaspoons of garlic until finely diced. Stir this fragrant mixture into the cooled roux, coating the vegetables evenly. Sauté for about 8-12 minutes until softened.

Gradually whisk in 10 cups of beef broth, ensuring no lumps remain from the roux. Increase heat to medium-high and bring to a boil, taking about 15-20 minutes.

Once boiling, reduce heat to low. Stir in sliced andouille sausage, stewed tomatoes, tomato sauce, hot sauce, white sugar, Cajun seasoning, thyme leaves, and bay leaves. Simmer uncovered for 45 minutes.

After 45 minutes, stir in gumbo filé powder and cook for another 15 minutes. Remove bay leaves, then add shrimp and Worcestershire sauce. Cook gently for 45-60 minutes, then serve.

Spoon the gumbo over bowls of cooked white rice and serve hot to enjoy.