Cook sausage: Place sausage in a large Dutch oven over medium; cook, stirring often, until browned on both sides, about 15 minutes. Using a slotted spoon, remove sausage to drain on paper towels; reserve drippings in pan.
Make roux: Add butter to hot drippings in Dutch oven, stirring until melted. Gradually whisk in all-purpose flour, and cook, whisking constantly, until mixture is caramel colored, 20 to 30 minutes.
Cook vegetables: Add onions, bell pepper, celery, and garlic, and cook, stirring often, until vegetables are very tender, 15 to 18 minutes.
Add broth, sausage, seasonings: Gradually stir in broth. Stir in sausage, okra, tomatoes, bay leaves, salt, Worcestershire sauce, hot sauce, thyme, and pepper.
Simmer gumbo: Increase heat to medium-high, and bring mixture to a boil. Reduce heat to low, and simmer, partially covered, stirring occasionally, about 3 hours.
Finish and serve: Remove and discard bay leaves. Stir in shrimp, and cook until shrimp turn pink, about 5 minutes. Stir in parsley, and remove from heat. Serve gumbo over hot cooked rice. Garnish with sliced scallions and filé powder, if desired.
