Preheat your grill to medium heat, about 350°F / 175°C, to ensure the shrimp cook evenly without burning the spices.
In a small bowl, whisk together the crushed garlic, coarse salt, paprika, cayenne pepper, lemon juice, and olive oil until the mixture forms a consistent, emulsified paste.
Place the peeled and deveined shrimp in a large bowl.
Pour the marinade over the top and toss gently until every shrimp is evenly coated.
Lightly brush the grill grates with olive oil to prevent sticking.
Arrange the shrimp in a single layer and grill for 2-3 minutes per side, until they are pink and opaque.
Remove the shrimp from the grill immediately to avoid overcooking.
Garnish with a generous squeeze of fresh lemon juice from the wedges and serve hot.
Pat your shrimp completely dry. Whether using fresh or thawed frozen shrimp, drying them with a paper towel is crucial. A dry surface allows the marinade to cling better and helps the shrimp sear rather than steam.