Combine broth, carrot juice, and 2 cups water in a 2-quart saucepan; bring to a simmer over medium-low heat.
Meanwhile, melt 1 tablespoon butter in a 3-quart saucepan over medium-low heat. Cook onion, stirring occasionally, until softened, 5 minutes. Season with 1 teaspoon salt and 1/4 teaspoon pepper.
Raise heat to medium; add rice and cook, stirring until grains are translucent around the edges, about 3 minutes. Stir in wine, if using; cook until absorbed, about 2 minutes.
Add 1/2 cup hot broth mixture, stirring with a wooden spoon until most liquid is absorbed. Continue adding broth, 1/2 cup at a time, stirring until it is incorporated and rice is tender but still a little firm to the bite, 25 to 30 minutes. Stir in remaining tablespoon butter and Parmesan. Season with salt and pepper. Divide among dishes, and sprinkle with parsley and more Parmesan.