Rinse and pat dry the scallops. Season with salt and pepper, then sprinkle the sugar on 1 side of the scallops, letting them sit until the sugar is slightly dissolved.
In a large skillet, melt 1 tablespoon butter into 1 tablespoon of olive oil over medium-high heat. Place scallops, sugar side down, into the skillet and cook for 2–3 minutes, or until browned. Flip and cook other side for 1–2 minutes more. Transfer to a plate and cover.
To make the sauce, melt 2 tablespoons butter into 1 tablespoon of olive oil over medium-high heat in the same skillet used for the scallops. Add garlic and lemon zest and cook for 2 minutes, stirring frequently. Season with salt and pepper. Add wine and let it reduce for 1–2 minutes. Drain the juices from reserved scallops into the pan, and let it reduce for 3 minutes. Add the lemon juice and cook for 1 minute more.
Serve the sea scallops in the lemon-butter sauce, sprinkled with the fresh parsley, with rice or pasta.