DO-AHEAD TIP: Marinate shrimp for 30 minutes (see recipe). If using bamboo skewers, soak them in water for 30 minutes before use, to prevent burning on the grill.
In a large zipper-topped plastic bag, place first 7 ingredients (olive oil through basil); shake to combine.
Add shrimp, seal bag and toss well to coat; refrigerate for 30 minutes. Preheat outdoor or indoor grill to HIGH.
Thread shrimp onto skewers and grill for 2 minutes per side or until pink and opaque.