Set oven control to broil. In medium glass or plastic bowl, mix lemon peel, lemon juice, red pepper, salt, garlic and 1 tablespoon of the oil. Add shrimp; toss to coat. In ungreased 15x10x1-inch pan, spread shrimp.
Broil shrimp with tops 2 to 3 inches from heat 3 to 5 minutes or until shrimp are pink and firm.
In food processor, place basil and remaining 2 tablespoons oil. Cover and process until chopped. Add mayonnaise; cover and process until smooth. Serve shrimp with mayonnaise.