Melt remaining 1/4 cup butter in a clean skillet; cook and stir flour in melted butter until smooth, about 3 minutes. Gradually stir in milk and season with salt and black pepper. Bring to a boil, stirring constantly, until thickened, about 2 minutes. Add Cheddar cheese; stir until melted. Pour cheese mixture over ham and potatoes. Sprinkle with bread crumbs.