The Ultimate Grilled Shrimp
Put a large grill pan on 2 burners over medium-high heat or preheat an outdoor gas or charcoal grill and get it very hot. If you're using an outdoor grill, take a few paper towels and fold them over several times to make a thick square. Blot a small amount of oil on the paper towel, then carefully and quickly wipe the hot grates of the grill to make a nonstick grilling surface.
Meanwhile, add the butter into a food processor with the basil leaves (reserve a few for garnish), the juice of 1 of the lemons, and salt and pepper. Puree. Stuff about half of the butter under the shells of the shrimp (about 1/2 tablespoon per shrimp). Lay the shrimp on the hot grill and cook for 3 minutes on each side, brushing with the remaining basil butter a few times as they cook.