Melt 3 tablespoons butter in a heavy saucepan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk and Worcestershire sauce; cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Add salt and pepper; stir well.
Process eggs through a food mill. Stir eggs into sauce. Spoon egg mixture into a lightly greased 1-quart casserole.
Combine breadcrumbs and butter, tossing well. Sprinkle over egg mixture. Bake at 350° for 30 minutes or until bubbly. Serve hot.