Melt 13 tablespoons of unsalted butter in a saucepan over medium-low heat. Once melted and foaming, add the smashed garlic cloves, freshly ground black pepper, and lemon zest strips. Let this infuse gently for 10 minutes, allowing the aromatics to release their flavors into the butter without browning. I like to keep the heat low here because if the garlic browns, it becomes bitter and overpowers the delicate shrimp. Use a spoon to skim off any white foam that rises to the surface—this improves the clarity and mouthfeel of the finished butter.

Remove the saucepan from heat and carefully pour the infused butter through a fine-mesh strainer into a shallow serving dish or bowl, discarding the garlic cloves and lemon zest. This leaves you with a clear, aromatic garlic butter that's ready to showcase the shrimp. Season with the flaky sea salt, stirring gently to incorporate.

Arrange the 1.5 pounds of large cooked tail-on shrimp around the edge of the garlic butter, or nestle them directly into the warm butter depending on your presentation preference. Drizzle the fresh lemon juice over the shrimp for brightness and acidity. I always serve the cocktail sauce in a small ramekin on the side—this lets guests decide how much they want and keeps the shrimp tender and not swimming in sauce. Serve immediately while the butter is still warm, providing small forks or cocktail picks for easy eating.