This recipe is a variation on the classic French dish, oeufs en cocotte, in which eggs are baked in a sauce in the oven. Served alongside toast and fruit, it makes an impressively easy breakfast for overnight guests.
Preheat oven to 350 degrees F. For sauce, in a small saucepan melt butter over medium heat. Stir in flour, 1/4 teaspoon salt, and 1/8 teaspoon pepper. If using, stir in dried basil. Add milk all at once. Cook and stir until thickened and bubbly. Cook and stir for 1 minute more. Remove from heat. If using, stir in 3 tablespoons fresh basil.
Lightly coat four 8- to 10-ounce round baking dishes or 6-ounce custard cups with cooking spray. To assemble, spoon about 2 tablespoons of the sauce into each prepared baking dish. Gently break an egg into the center of each dish; sprinkle with additional salt and pepper. Spoon the remaining sauce over eggs.
Bake for 18 to 20 minutes or until eggs are set. Sprinkle with cheese. Let stand until cheese is melted. If desired, garnish with additional fresh basil.