In a food processor pulse basil, garlic, parmesan cheese, salt and pepper until smooth. Slowly add the olive oil while pulsing.

Combine raw shrimp with pesto and marinate a few hours in a bowl. Soak wooden skewers in water at least 20 minutes (or use metal ones to avoid this step). Thread shrimp onto skewers. 

Heat an outdoor grill or indoor grill pan over medium-low heat until hot. Be sure the grates are clean and spray lightly with oil. Place the shrimp on the hot grill and cook until shrimp turns pink on the bottom, about 3-4 minutes; turn and continue cooking until shrimp is opaque and cooked through, about 3-4 minutes.