In a large 6-quart pot, melt ¾ cup of unsalted butter over medium-low heat. Whisk in 1 cup of all-purpose flour, stirring constantly for 30 to 40 minutes until it transforms into a deep, chocolate brown color.

Remove the pot from heat and set it aside. In a food processor, finely chop 2 ribs of celery, 1 large yellow onion, 1 green bell pepper, and 2 teaspoons of minced garlic. Stir this fresh vegetable mix into the roux, and return the pot to medium heat. Cook for 8 to 12 minutes until the vegetables are tender and fragrant.

Gradually whisk in 10 cups of beef broth, bringing the mixture to a boil over medium-high heat—this should take about 15 to 20 minutes. Once boiling, reduce the heat to low and stir in the sliced andouille sausage, 1 can of stewed tomatoes, 1 can of tomato sauce, 2 tablespoons of hot sauce, 1 tablespoon of sugar, and ½ teaspoon each of Cajun seasoning and dried thyme. Add 4 bay leaves, then simmer uncovered for 45 minutes to let the flavors meld.

Carefully stir in 2 teaspoons of gumbo filé powder and cook for an additional 15 minutes to thicken the gumbo further. Then, add 3 pounds of medium shrimp and 2 tablespoons of Worcestershire sauce, cooking everything over low heat for 45 to 60 minutes.

Before serving your gumbo, stir in the remaining 2 teaspoons of gumbo filé powder. Ladle the hearty gumbo over bowls of cooked white rice to make it a complete meal.