Preheat an oven. Place the shrimp on a sheet pan, then drizzle with olive oil, Old Bay, and kosher salt.
Transfer to the oven and cook until the shrimp turn pink and are fully cooked. While the shrimp cook, make the sauce.
Combine Ketchup, chili sauce, horseradish, fresh lemon juice, hot sauce, gin, and Worcestershire sauce in a bowl. Whisk to combine, then refrigerate until needed.
The shrimp can be enjoyed immediately or chilled for later. Serve with a sprinkle of chopped parsley, lemon wedges, and the cocktail sauce. Enjoy!