Heat the broiler to high and set an oven rack 6 inches from the heat source. Line a large sheet pan with aluminum foil.
Pat the shrimp very dry with paper towels. Thread onto 8 skewers, dividing them evenly (4 to 5 per skewer) and packing the shrimp snugly together; use metal skewers, or soak wooden skewers 30 minutes first.
In a small bowl, stir together the melted butter, olive oil, garlic, lemon zest, 1 tbsp of the lemon juice, smoked paprika, salt, black pepper and red pepper flakes.
Brush the skewers generously on both sides with about two-thirds of the butter mixture.
Broil for 3 minutes, flip once, and broil 2 to 3 minutes more, until the shrimp are opaque and firm and an instant-read thermometer in the thickest part reads 145°F.
Brush with the remaining butter, squeeze the last 1 tbsp lemon juice over the top, scatter with parsley and serve warm.