Preheat the oven to 350°F (177°C).
In a large skillet, over medium heat, melt the 4 sticks (1 pound) unsalted butter, stir in the 1/4 cup extra-virgin olive oil, and add the 1 medium (2 oz) shallot and minced 8 cloves garlic. Simmer until the shallot is translucent and the garlic turns golden, 2 to 3 minutes.
Whisk in the 1/2 cup Worcestershire sauce, 1 teaspoon finely chopped fresh thyme, 1 teaspoon finely chopped fresh oregano, 1 teaspoon finely chopped fresh flat-leaf parsley, 2 tablespoons fresh lemon juice, 1/2 teaspoon cayenne pepper, 1 tablespoon sweet paprika, and 1 tablespoon Creole seasoning. Reduce the heat to low and simmer for 10 minutes to let the flavors meld. Add the 3 bay leaves and continue to simmer until dark and slightly thickened, about 15 minutes more.
Pile the 3 pounds (18 to 20 count) jumbo shrimp in a 9-by-13-inch (23-by-33-cm) baking dish or roasting pan, pour the sauce over the shrimp, and bake for 10 minutes. Flip the shrimp, stir, and bake until cooked through, about 5 minutes more.
Remove from the oven, discard the bay leaves, and let sit for 5 minutes before serving with rice, bread, or biscuits, if desired.