In a large skillet, cook bacon until crisp. Remove bacon and set aside; discard all but 2 tablespoons of drippings. Saute mushrooms and onions in drippings until tender; set aside.
In a large saucepan, melt butter. Stir in the flour, salt and pepper until smooth; cook until bubbly. Gradually stir in milk and cheese; cook and stir until thickened. Stir in the bacon, mushrooms and onions; remove from the heat and set aside.
For scrambled eggs, beat the eggs, milk, pepper and salt; pour into a greased skillet. Cook and stir gently until eggs are set. Remove from the heat and set aside.
Cut English muffin halves in half again. Place in a greased 11-in. x 7-in. baking dish. Cover with half of cheese sauce. Spoon eggs over all; top with remaining sauce. Sprinkle with parsley.
Bake, uncovered, at 325° for 20-25 minutes or until bubbly.