Start by melting the butter in a large 6-quart pot set to medium-low. Stir in the flour and whisk continuously until the mixture turns a rich, deep brown color, which should take around 30-40 minutes – be careful to avoid burning it.
Take the pot off the heat and keep whisking the roux to cool it down a bit, then set it aside.
While the roux cools, finely chop the celery, onion, bell pepper, and garlic using a food processor.
Add the chopped veggies into the roux and stir to combine, then return the pot to medium-low heat and cook until the vegetables soften, about 8 to 12 minutes.
Slowly pour in the beef broth while whisking and bring the stew to a boil, this will take around 15-20 minutes.
Turn the heat down to low, then mix in the sliced sausage, stewed tomatoes, tomato sauce, hot sauce, sugar, Cajun seasoning, and dried thyme. Add the bay leaves and let the gumbo simmer uncovered for 45 minutes.
After that, stir in 2 teaspoons of gumbo filé powder, and keep simmering for another 15 minutes.
Remove the bay leaves, then toss in the shrimp and Worcestershire sauce. Let it cook gently on low heat for 45 to 60 minutes so all the flavors blend beautifully.
Finally, stir in the remaining gumbo filé powder.
Serve the gumbo hot over freshly cooked white rice.
