This recipe calls for cheddar cheese, but you can switch in any favorite. Add a few strips of cooked bacon if you wish.
Preheat oven to 350 degrees. Cut bread horizontally. Lightly toast in oven, cut sides up. Top with cheese (1 slice on each side), and continue to cook in oven until cheese melts, 1 to 2 minutes. Meanwhile, fry eggs in butter; season with salt and pepper.
Place eggs on bottom half of bread. Top with tomatoes and basil. Sandwich with top bread half, and press down slightly. Wrap tightly in parchment.