In a mixing bowl, whisk together the melted butter, lemon juice, and minced parsley; set the butter mixture aside.
Pat the shrimp dry with paper towels. Sprinkle the shrimp evenly with 1/4 teaspoon salt, 1/4 teaspoon pepper, and the 1/8 teaspoon sugar.
Heat 2 teaspoons of the olive oil in a 12-inch nonstick skillet over medium-high heat until shimmering.
Add half the minced garlic and half the shrimp to the skillet; cook, turning once, until the shrimp are opaque and cooked through, about 3 minutes total.
Transfer the cooked shrimp to a piece of foil and wrap to keep warm. Wipe the skillet if needed, then repeat the cooking with the remaining 2 teaspoons oil, remaining garlic, and remaining shrimp.
Return all the shrimp to the skillet, pour the reserved butter-lemon-parsley mixture over them, and toss gently to coat. Serve warm.