Put a large grill pan on two burners over medium-high heat or pre-heat an outdoor gas or charcoal grill and get it very hot. ¬†If you‚Äôre 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, throw the butter into a food processor with the basil leaves (reserve a few for garnish), the juice of one of the lemons, and salt and pepper. ¬†Puree. ¬†Stuff about half of the butter under the shells of the shrimp (about ¬Ĺ 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.
To serve, put the shrimp on plates and dot with the remaining basil butter. ¬†Squeeze the remaining lemon over the shrimp and garnish the plates with basil leaves.
Edited: October 2nd, 2009