Pulse all pesto ingredients in a food processor until they form a paste. Remove and set aside.

Place shrimp in a single layer in a baking dish. In a small mixing bowl, whisk together olive oil, red pepper flakes, lemon juice and thyme; pour over shrimp. Set aside for 30 minutes.

When ready to cook, preheat grill to medium heat and lightly oil the grates to prevent sticking. Skewer shrimp onto rosemary sprigs and grill for 5 to 6 minutes per side or until pink. Arrange skewers on a serving platter and serve with Lemon Garlic Pesto.