In a bowl, combine the melted butter, minced garlic, garlic powder, smoked paprika, cayenne pepper, kosher salt, lemon zest, and fresh parsley, stirring until well blended. Reserve ¼ cup of this aromatic butter mixture in a separate small bowl for finishing the shrimp after grilling. Add the olive oil to the remaining butter mixture and toss the thawed shrimp in it until evenly coated, ensuring every piece gets flavor.
While heating your grill to medium-high heat, thread the butter-coated shrimp from Step 1 onto metal or wooden skewers (if using wooden skewers, soak them in water for 15 minutes first). Pack them snugly on the skewers so they cook evenly and don't spin around during grilling. I like to thread the shrimp through both the tail and body to keep them secure and prevent them from curling too tightly.
Place the skewers directly on the grill grates and cook for 3-4 minutes without moving them—this allows the shrimp to develop a beautiful char and golden color on the first side. Flip the skewers carefully and grill for another 3-4 minutes on the second side. The shrimp are done when they're opaque throughout and have a slight pink color; avoid overcooking or they'll become rubbery.
Remove the skewers from the grill and brush the hot shrimp generously with the reserved garlic butter mixture from Step 1, allowing it to melt into the crevices and coat each piece. Transfer to a serving platter and serve immediately with the lemon wedges on the side for squeezing over the top. I always serve this dish hot right off the grill—the butter stays silky and the shrimp are at their most tender.