Bring water to a boil in large frying pan. Add potatoes, carrots and onions. Cover and cook for 10 minutes or until tender; drain. In another saucepan, melt butter then remove from heat. Stir in flour, salt and peppers. Add milk, blending well. Bring to a boil over medium heat, stirring until thickened and smooth. Stir in cheese and cook over low heat, stirring constantly until cheese melts. Layer half of the potatoes, onions and carrots in lightly greased 9x13 baking dish. Top with half the sauce. Repeat layers. Bake covered for 30 minutes or until potatoes are tender. Remove cover during the last 10 minutes of baking. Serves 6-8.