Everyone knows that a Monte Cristo sandwich is sort of a French toast sandwich, only savory, so I combine it with America's favorite ground beef dish, the burger.
- Preheat oven to 200 degrees.
- Combine the egg, hot sauce, and cream in a pie plate. Dip cut sides of buns into egg mixture. Move to a cooling rack and let sit 10 minutes.
- Heat a medium nonstick skillet over medium heat. Grease with nonstick cooking spray.
- Add buns, one at a time, and cook until browned on cut side. Move to a clean plate and repeat until all buns have been cooked. Keep warm in the oven.
- Form beef into 4 equal patties. Brush both sides with olive oil and sprinkle both sides liberally with salt and freshly ground black pepper.
- Heat about 28 charcoal briquets in a large chimney starter. Once hot, disperse evenly around the bottom of the grill and reapply grate. Add patties and cook, turning often, until internal temperature reaches 145 degrees F for medium rare, 160 for medium, and 170 for toast. (I know people think 165F is the only way to be safe, but I'm taking my chances.)
- Remove to a plate, top with cheese, and cover with aluminum foil. Let rest 3 minutes.
- Place a patty on the bottom half of each bun. Top with upper half and serve warm.