Brown sausage or ham in a Dutch oven over medium heat. Transfer to a paper towel to drain.
Drain the rendered fat from the pot and add 4 tablespoons (1/2 stick butter) and 1/4 cup vegetable oil. Once the butter has melted, whisk in 1/2 cup all-purpose flour a little at a time. Cook, stirring constantly with a wooden spoon or whisk until the roux turns dark mahogany brown, about 20 minutes.
Add onions, celery, and green bell pepper and cook, stirring, until softened, about 10 minutes. Add garlic, jalapeno or serrano peppers, bay leaf, 1 tsp salt, 1 tsp pepper, dried thyme, dried oregano, and cayenne pepper. and cook, stirring, for another 3 minutes.
Add 5 cups shrimp or shellfish stock, or chicken stock. Bring to a boil, add the reserved browned sausage, and simmer for 20 minutes.
Add peeled shrimp, lump crab meet, and okra. Return to a boil, then reduce the heat and simmer for another 10 minutes.
Add oysters. Cook just until the oysters are plump. Season with salt and pepper.
Serve over cooked jasmine rice. Sprinkle with chopped parsley and chopped green onion.