In a large saucepan, melt butter over medium heat. Whisk in the flour, salt and pepper until smooth. Gradually stir in milk. Bring to a boil; cook and stir for 2 minutes or until thickened. Reduce heat; add 1/2 cup cheese, stirring until melted. Add the potatoes, carrots and onion.
Transfer to a greased 8-in. square baking dish. Cover and bake at 350° for 1 hour. Sprinkle with the remaining cheese. Bake, uncovered, for 15 minutes longer or until potatoes are tender.