In a large 6-quart pot over medium-low heat, melt ¾ cup of unsalted butter until bubbling. Gradually whisk in 1 cup of all-purpose flour and cook, stirring constantly, until the mixture turns a rich mahogany color, about 30-40 minutes.

Once the roux reaches the desired color, remove the pot from heat for a moment to cool slightly. Carefully stir in 1 cup each of chopped celery, onion, and green bell pepper, along with 2 teaspoons of minced garlic. Return the pot to medium-low heat and cook for 8-12 minutes until the vegetables are tender and fragrant.

Slowly whisk in 10 cups of beef broth, ensuring no lumps form as you bring the mixture back to a boil over medium-high heat. This step will blend the roux and vegetable flavors.

After reaching a boil, reduce the heat to a low simmer and add the sliced 14 ounces of andouille sausage, the 14.5-ounce can of stewed tomatoes, 6-ounce can of tomato sauce, 2 tablespoons of hot sauce, 1 tablespoon of white sugar, ½ teaspoon of Cajun seasoning, ½ teaspoon of dried thyme, and 4 bay leaves. Allow the gumbo to simmer uncovered for 45 minutes.

Stir in 2 teaspoons of gumbo filé powder into the pot and let the mixture simmer again for an additional 15 minutes.

Remove the bay leaves carefully from the pot before adding 3 pounds of uncooked shrimp and 2 tablespoons of Worcestershire sauce. Reduce the heat to low and let the gumbo cook for another 45-60 minutes, stirring occasionally.

To finish off your gumbo, stir in the remaining 2 teaspoons of gumbo filé powder for added richness. Taste and adjust seasoning if needed, then serve this comforting dish hot over fluffy white rice.