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. Stir in salt and pepper.
Layer half of salmon and egg in a lightly greased 1-quart casserole; pour half of white sauce evenly over top. Repeat procedure with remaining salmon, egg, and white sauce; sprinkle bread cubes over top.
Bake at 350° for 25 minutes or until bubbly and lightly browned.