Slice 1 1/2 lb. carrots diagonally, about 1/4-inch thick. Place in a large saucepan and pour in water to cover. Add 1/2 tsp. salt and bring to a boil over high heat. Reduce heat to medium and cook until almost tender, about 3 minutes. Drain and rinse carrots under cold running water.
In a large skillet, melt 2 Tbsp. unsalted butter over medium-high heat. Add 1 chopped garlic clove and cook, stirring, until fragrant, about 1 minute. Add 1 chopped 2-inch piece fresh ginger and cook 2 minutes longer. Add carrots and 1 tsp. sugar. Stir until tender and shiny, about 5 minutes. If carrots begin to stick, add 1 or 2 tsp. water. Season with salt and pepper. Sprinkle with 1 Tbsp. chopped fresh parsley just before serving.