Carrots and Brussels Sprouts

Cook shallot in 2 tablespoons butter in a 12-inch heavy skillet over medium-high heat, stirring occasionally, until softened, 1 to 2 minutes. Add carrots, Brussels sprouts, 3/4 teaspoon salt, and 1/2 teaspoon pepper and cook, stirring occasionally, until vegetables begin to brown, 3 to 4 minutes. Add water and cover skillet, then cook over medium-high heat until vegetables are tender, 5 to 8 minutes. Stir in vinegar, remaining tablespoon butter, and salt and pepper to taste.