Beat butter with a fork in a small bowl until light and fluffy. Stir in garlic, lemon juice, parsley and 1/8 tsp salt until combined. Set aside.
Heat 1 tbs oil in a 12-inch skillet over high heat until smoking. Meanwhile toss shrimp, salt, pepper and sugar in a medium bowl. Add half of shrimp to pan in a single layer and cook until spotty brown and edges turn pink, about 1 minute. Remove pan from heat; using tongs, flip each shrimp and let stand until all but very center is opaque, about 30 seconds. Transfer shrimp to a large plate.
Repeat with remaining oil and shrimp; after second batch has stood off heat, return first batch to skillet along with flavored butter and toss to combine. Cover skillet and let stand until shrimp are cooked through, 1 to 2 minutes. Serve with lemon wedges if desired.