Season and Cook the Shrimp
Season the shrimp with seafood seasoning. Heat 2 tablespoons of vegetable oil in a skillet over medium-high heat. Add the shrimp and cook for 2-3 minutes on each side until they turn pink and opaque. Remove from the skillet and set aside to prevent overcooking while you prepare the rest of the dish.
Brown the Meats
Heat the remaining tablespoon of vegetable oil in a large skillet over medium heat. Add the hamburger meat and ground pork sausage, breaking them apart with a wooden spoon. Cook until fully browned, about 8-10 minutes. Add the chopped onions, bell peppers, and minced garlic to the meat mixture. Continue cooking for another 5 minutes until the vegetables have softened and become fragrant.
Season and Thicken the Mixture
Sprinkle all the dry seasonings over the meat and vegetable mixture – oregano, thyme, garlic powder, onion powder, chili powder, pepper, salt, and cayenne pepper if using. Stir well to evenly distribute the spices. Sprinkle the flour over the mixture and stir continuously for about 2 minutes to cook off the raw flour taste. Gradually pour in the chicken broth while stirring to prevent lumps from forming. Allow the mixture to simmer for 5-7 minutes until it thickens to a gravy-like consistency.
Combine with Rice and Finish the Dish
Add the cooked rice to the skillet, folding it into the meat mixture until well combined and evenly coated with the sauce. Gently fold in the reserved cooked shrimp, being careful not to break them. Let everything heat through for 2-3 minutes. Taste and adjust seasonings if necessary before serving hot.