In a small bowl, combine the basil, oil, butter, mustard, lemon juice, garlic, salt and pepper. Pour 3 tablespoons into a small resealable plastic bag; add shrimp. Seal bag and turn to coat; let stand at room temperature for 15-20 minutes. Set remaining marinade aside.
Drain and discard marinade. Thread shrimp onto two metal or soaked wooden skewers. Grill, covered, over medium heat for 2-3 minutes on each side or until shrimp turn pink, basting occasionally with reserved marinade.