Start by rinsing the shrimp under cold water. If using frozen shrimp, ensure they are fully thawed. Peel and devein the shrimp, leaving the tails intact for presentation.
In a mixing bowl, combine the shrimp with salt and black pepper. Gently toss to coat the shrimp evenly with the seasoning.
Using a small spoon or a piping bag, carefully stuff each shrimp with the sun-dried tomato pesto. Be generous but ensure the pesto stays inside the shrimp without overflowing.
If you choose to bake, preheat your oven to 400°F (200°C). If grilling, preheat your grill to medium-high heat. Lightly grease your baking sheet with cooking spray or brush the grill grates with olive oil.
Place the stuffed shrimp on the baking sheet or grill. Drizzle the extra virgin olive oil over the shrimp for added flavor and moisture. Bake for 10-12 minutes or grill for about 2-3 minutes per side, until the shrimp are cooked through and opaque.
Once cooked, remove the shrimp from the heat. Serve immediately with fresh lemon wedges and perhaps a sprinkle of fresh herbs for garnish.