Melt butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk; cook over medium heat, stirring constantly, until thickened and bubbly. Add salt and pepper, mixing well.
Layer half each of asparagus spears, white sauce, breadcrumbs, and cheese in a lightly greased 10- x 6- x 2-inch baking dish. Repeat layers, reserving cheese. Set cheese aside.
Bake at 350° for 20 minutes; sprinkle with remaining cheese, and continue baking 5 minutes or until cheese melts. Serve hot.