Melt Butter In A Large Saucepan Over Medium Heat. Whisk In Flour To Make A Roux, And Cook For 10 Minutes Until The Roux Begins To Lighten In Color. Whisk In The Milk, And Bring To A Simmer, Whisking Constantly. Reduce Heat To Medium-Low, And Cook For 10 Minutes More, Whisking Occasionally. Season To Taste With Salt And Pepper. Separate The Hard-Cooked Egg Whites From The Yolks. Roughly Chop The Whites And Stir Into The White Sauce. Press The Yolks Through A Mesh Strainer And Set Aside. To Serve, Place A Slice Of Toast On A Plate, And Ladle 1/2 Cup Of White Sauce Over Top. Garnish With Egg Yolks And A Sprinkle Of Paprika.