In a bowl, combine the olive oil, minced garlic, lemon zest, lemon juice, smoked paprika, salt, and black pepper. Add the shrimp and toss to coat thoroughly. Cover and let marinate in the refrigerator for at least 30 minutes.
If using wooden skewers, soak them in water for 30 minutes to prevent burning. Preheat your grill or grill pan over medium-high heat.
Thread the marinated shrimp onto the skewers, about 4-5 shrimp per skewer, leaving a little space between each shrimp for even cooking.
Place the skewers on the preheated grill. Cook for 2-3 minutes on each side or until the shrimp are pink and opaque, and slightly charred.
Once cooked, remove the skewers from the grill and sprinkle with freshly chopped parsley for garnish. Serve with extra lemon wedges on the side.