Cook the carrots and ½ cup water in a large skillet, covered, over medium-high heat, until crisp-tender, 6 to 8 minutes.
Add the ginger, sugar, 2 tablespoons of butter, ¾ teaspoon salt, and ½ teaspoon pepper. Cook, uncovered, stirring occasionally, until the liquid coats the carrots, 2 to 3 minutes.
Stir in the vinegar and the remaining 2 tablespoons of butter. Serve warm.