In a food processor blend together the garlic, mayonnaise and lemon juice. Remove to a small serving bowl and stir in the chives.
For the roasted garlic dipping sauce: Heat a cast-iron grill pan.
Add the garlic, rosemary, olive oil, lemon juice, red pepper flakes, salt and pepper together in a large bowl. Add the shrimp and toss to coat. Let the shrimp sit at room temperature 15 minutes.
For the grilled rosemary shrimp: Skewer the shrimp on the bamboo skewers, about 3 per skewer. Grill the shrimp until cooked through, about 3 minutes on each side. Place the skewers on the platter and garnish with rosemary sprigs. Serve the shrimp with the roasted garlic dipping sauce.
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