In a zip-lock bag, combine ½ cup brown sugar, ¼ cup rum, and 1 tablespoon cinnamon. Add pineapple wedges, seal the bag, and shake to ensure the wedges are evenly coated. Let the pineapple marinate for 15 minutes at room temperature.

In a medium bowl, mix together 2 finely chopped garlic cloves, ¼ cup chopped basil leaves, 3 tablespoons lemon juice, 3 tablespoons olive oil, and a pinch of salt and pepper. Reserve 2 tablespoons of this marinade for dipping later. Add the peeled and deveined shrimp to the bowl, coating them thoroughly, and let them sit for 15 minutes to soak up the vibrant flavors.

Using the rosemary sprigs as skewers, first strip the leaves from the bottom third of each sprig. Thread the marinated shrimp onto the rosemary skewers, alternating with the marinated pineapple wedges to create a colorful and aromatic display.

Preheat your grill to medium-high heat, aiming for around 400°F. Place the pineapple skewers on the grill and cook for 3-5 minutes per side, turning carefully. Once done, transfer to a warm plate.

Place the shrimp skewers on the grill and cook for 2 minutes per side until opaque and firm. Be cautious as they cook quickly.

Arrange the beautifully grilled skewers on a serving platter alongside the reserved marinade for dipping.