In a small bowl or jar, combine the olive oil, lime juice, minced garlic, Worcestershire sauce, and honey. Whisk until the honey dissolves completely and the mixture is well combined. Add the kosher salt, black pepper, smoked paprika, and red pepper flakes, stirring to distribute the spices evenly. Taste the marinade and adjust seasoning if needed—it should be balanced between acidic (lime), savory (Worcestershire), and slightly sweet (honey). Stir in the fresh parsley just before using.
Place the peeled and deveined shrimp (tails on) in a bowl or zip-top bag. Pour the marinade from Step 1 over the shrimp and gently toss to coat evenly, making sure all shrimp are submerged or well coated. Cover the bowl or seal the bag and refrigerate for 15-20 minutes. I find that shrimp don't need much longer than this—their delicate texture absorbs the flavors quickly, and marinating too long can make them mushy.
While the shrimp marinates, preheat your grill or broiler to medium-high heat (around 400-450°F for a grill, or position the oven rack 4-6 inches from the broiler element). If using wooden skewers, soak them in water for at least 10 minutes to prevent burning. Once the marinating time is complete, remove the shrimp from the marinade and discard the remaining liquid.
Thread the marinated shrimp onto skewers (about 5-6 shrimp per skewer), alternating direction if desired for even cooking. Place the skewers directly on the grill grates or on a broiler pan. Cook for 2-3 minutes on the first side without moving them—this creates a nice caramelized exterior. Flip the skewers and cook for another 2-3 minutes until the shrimp are opaque and cooked through. I like to slightly rotate them on the second side to create beautiful grill marks. Shrimp cook fast, so watch carefully to avoid overcooking and keep them tender.
Transfer the grilled shrimp skewers to a serving platter. Sprinkle with extra chopped fresh parsley and arrange fresh lime wedges alongside for squeezing over the shrimp. Serve immediately while still warm.