In 1-quart nonstick saucepan, melt butter over low heat. Stir in flour; remove from heat. Gradually stir in milk. Heat to boiling, stirring constantly. Boil and stir 1 minute; remove from heat. Stir in cheeses, basil and red pepper; keep warm.
Toast English muffins. In 10-inch nonstick skillet, cook bacon over medium heat until brown on both sides. Remove from skillet; keep warm.
Heat same skillet over medium heat. Pour eggs into skillet. As mixture begins to set at bottom and side, gently lift cooked portions with spatula so that thin, uncooked portion can flow to bottom. Avoid constant stirring. Cook 3 to 4 minutes or until eggs are thickened throughout but still moist.
Place 1 slice bacon on each muffin half. Top with eggs. Spoon about 2 tablespoons sauce over eggs. Sprinkle with pepper.