In a saucepan melt butter, stir in flour, until smooth, gradually add milk bring to a boil, cook and stir for 2 minutes or until thickened, stir in cheese. Put potatoes, ham and carrots in a greased 2 qt. pan, pour sauce over, stir to coat. Voer and bake at 350 for 30 minutes. Uncover, bake 15-20 minutes longer or until golden brown.