Separate the whites and yolks of cooked eggs, dice the whites, set aside yolks.
Place butter in saucepan, and melt over medium heat.
Stir in flour, stirring constantly, until butter and flour are well blended; then cook over low heat stirring at least 2 minutes more.
Slowly add milk, stirring constantly and cook for 5 minutes.
Stirring until sauce has thickened, add salt and pepper to taste.
Add the diced egg white to the sauce.
Place toasted english muffin halves on serving plates, spoon sauce over muffins.
Using a fine grater, grate egg yolks over each portion.
Serve hot.
