Instructions

• Brush the steaks on both sides with 2 tablespoons oil. Season evenly with 1½ teaspoons salt and ¾ teaspoon pepper. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.

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• Prepare the grill for direct cooking over high heat (450° to 550°F) and preheat a grill-proof griddle for 10 minutes.
• In a bowl mix the onion and bell pepper with 1 tablespoon oil. In another bowl mix the mushrooms with 1 tablespoon oil. Spread the onion and bell pepper in a single layer on the griddle and cook until softened, about 5 minutes, stirring occasionally. Push the onion and bell pepper to one side of the griddle. Add the mushrooms to the griddle and cook them until the juices evaporate and the mushrooms are beginning to brown, about 8 minutes, stirring occasionally. Remove the vegetables from the griddle and season with salt and pepper. Cover and keep warm.
• Grill the steaks on the cooking grate over direct high heat, with the lid closed, for 1½ to 2 minutes, turning when the first side is nicely marked. The second side will only take about 30 seconds to reach medium-rare doneness. Remove from the grill. Toast the rolls, cut side down, over direct high heat, for about 1 minute. Remove from the grill and immediately top each roll with two slices of cheese.
  Grill the steaks on the cooking grate over high heat, with the lid closed, for 1½ to 2 minutes, turning when the first side is nicely marked. The second side will only take about 30 seconds to reach medium-rare doneness. Remove from the grill. Toast the rolls, cut side down, over high heat, for about 1 minute. Remove from the grill and immediately top each roll with two slices of cheese.
• To assemble, place a steak in each roll and top with an equal amount of the vegetables. Warm the sandwiches on the griddle until the outsides are crusty. If desired, flatten the sandwiches with a grill press. Serve warm.