Cut the shrimp in half lengthwise. Mince the garlic. Shred the basil leaves. Toss together with the shrimp halves and the olive oil in a glass bowl. Cover and let sit in the fridge for about an hour. Remove half an hour before cooking.
Heat the oven to broil. Spread the shrimp over a baking sheet, dribbling over any basil oil that stays behind in the bowl. Broil 5 minutes until the flesh is cooked. Serve immediately, if not sooner.