In a large Dutch oven or stockpot, heat the vegetable oil over medium heat. Gradually whisk in the flour, stirring constantly, until the mixture is smooth.
Continue cooking the oil and flour mixture, stirring frequently, for about 20-25 minutes, until it turns a dark brown color (this is known as making a roux).
Add the onion, bell pepper, and celery to the pot, and cook for about 5-7 minutes, until the vegetables are softened.
Add the garlic, and cook for another 1-2 minutes, until fragrant.
Pour in the seafood or chicken broth, and stir well to combine. Add the diced tomatoes, bay leaves, thyme, oregano, paprika, salt, and black pepper, and bring the mixture to a boil.
Reduce the heat to low, and let the gumbo simmer for about 30-40 minutes, until the flavors have melded together and the broth has thickened slightly.
Add the shrimp, crab meat, and shucked oysters to the pot, and cook for another 5-7 minutes, until the seafood is cooked through.
Stir in the chopped green onions and hot sauce, to taste.
Serve the seafood gumbo hot, over a bed of cooked white rice.
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