Wrap each steak individually in plastic wrap, place them in the freezer, and freeze for about 3 hours; this will make it easier to slice the meat.

Remove 1 steak from the freezer and use a very sharp knife to slice it as thin as you can, discarding any pockets of fat. Set aside, and repeat with the other steak.

Preheat the oven to 300°F.

Slice open the French bread, and set it aside on a large baking sheet.

Arrange the cheese in four overlapping piles on a large serving platter, alternating slices of provolone and American.

Heat 2 tablespoons of the olive oil in a large cast-iron skillet set over medium-high heat. Add the onion and bell pepper, 1 teaspoon of the salt, and 1/4 teaspoon of the black pepper. Cook, stirring occasionally, until the onion is lightly caramelized and tender, about 8 minutes. Stir in the cherry peppers, and then transfer the onion and peppers to the same baking sheet with the bread, and place in the oven to keep warm while you cook the steak.

Making 2 sandwiches at a time, increase the heat under the skillet to high and add 1 tablespoon oil. Add half the steak slices, season them with 1/2 teaspoon salt and 1/4 teaspoon pepper, and cook without stirring until most of the meat has browned on one side, about 1 minute. Stir the meat, and then divide it into two cylindrical portions. Lay a shingled pile of cheese over each pile of meat. Remove the baking sheet from the oven and spoon one-quarter of the onion and peppers over each cheese-topped meat pile. Continue to cook in the skillet, undisturbed, for 1 minute longer, or until the cheese begins to melt from the heat of the vegetables. Using a large spatula, transfer each of the meat portions to a bottom half of the bread. Set the 2 filled sandwiches on a small baking sheet and place them in the oven to keep warm. Wipe the skillet clean and repeat to make the other 2 sandwiches.