Step 1: Prepare the Shrimp. If using head-on, carefully remove the heads (optional, but they add flavor). Rinse the shrimp and pat them very dry with paper towels. Do not peel the shells, as they infuse flavor into the sauce and protect the shrimp.
Step 2: Create the Flavor Base. In a large (12-inch or larger) heavy-bottomed skillet or Dutch oven, melt 2 tablespoons of unsalted butter over medium-high heat. Add the minced garlic and cook for about 30-60 seconds until fragrant, being careful not to let it brown.
Step 3: Add Liquids and Seasoning. Stir in the Worcestershire sauce, 1 tablespoon of lemon juice, fresh ground black pepper, and Cajun/Creole seasoning. Cook for 1 minute, stirring constantly, allowing the spices to bloom. Add the chicken or shrimp stock and bring to a gentle simmer.
Step 4: Cook the Shrimp. Increase the heat to high. Add the shrimp to the skillet in a single layer. Cook for 1-2 minutes per side, just until they start to turn pink and opaque. Do not overcook. If your pan is not large enough to hold all shrimp in a single layer, cook in two batches.
Step 5: Emulsify the Sauce. Once the shrimp are almost cooked through, reduce the heat to low. Add the remaining 1/2 cup of cold, cubed unsalted butter, a few cubes at a time, whisking constantly until each batch is melted and incorporated before adding more. This process creates a rich, emulsified, and glossy sauce.
Step 6: Finish and Serve. Stir in 1/4 cup of fresh chopped parsley. Taste and adjust seasoning if necessary, adding a splash more lemon juice if desired. Transfer the New Orleans Buttery BBQ Shrimp and all the delicious sauce immediately to a large serving platter. Garnish with additional fresh parsley and serve hot with plenty of crusty French bread for dipping.