Heat oven to 425° F. Rub the potatoes with the oil and season with ¼ teaspoon each salt and pepper. Bake, cut-side down, on a rimmed baking sheet, until golden brown and tender, 18 to 22 minutes.
Turn oven to broil. Combine the fontina and Parmesan in a small bowl. Turn the potatoes cut-side up and top with the cheese mixture, dividing evenly. Broil until the cheese is melted and golden brown, 2 to 3 minutes. Sprinkle with more pepper, if desired. Serve warm.