Prepare the grill for direct cooking over high heat (230° to 290°C) and preheat a grill pan.
Prepare the grill for cooking over high heat (260°C) and preheat a grill pan.
In a large bowl combine the onion, peppers, garlic, oil, and oregano. Season with salt and pepper and toss to coat evenly. Spread the vegetables on the grill pan in a single layer. Grill over direct high heat, with the lid closed, until they start to brown and are tender, about 6 minutes, stirring occasionally. Wearing insulated barbecue mitts or gloves, transfer the vegetables to a medium bowl. Return the grill pan to the grill.
In a large bowl combine the onion, peppers, garlic, oil, and oregano. Season with salt and pepper and toss to coat evenly. Spread the vegetables on the grill pan in a single layer. Grill over high heat, with the lid closed, until they start to brown and are tender, about 6 minutes, stirring occasionally. Wearing insulated barbecue mitts or gloves, transfer the vegetables to a medium bowl. Return the grill pan to the grill.
Cut the steaks across the grain into 3-millimeter slices. Place the slices in a medium bowl, add just enough oil to coat them lightly, and season with salt and pepper; turn to coat. Grill the steak slices on the grill pan over direct high heat, with the lid closed, until the meat begins to curl and brown, 4 to 6 minutes, turning occasionally. Wearing insulated barbecue mitts or gloves, remove the pan from the grill and add the meat to the vegetables.
Cut the steaks across the grain into 3-millimeter slices. Place the slices in a medium bowl, add just enough oil to coat them lightly, and season with salt and pepper; turn to coat. Grill the steak slices on the grill pan over high heat, with the lid closed, until the meat begins to curl and brown, 4 to 6 minutes, turning occasionally. Wearing insulated barbecue mitts or gloves, remove the pan from the grill and add the meat to the vegetables.
Lightly brush the cut side of the rolls with oil, and then grill over direct high heat until toasted, about 30 seconds. Gently rub the garlic onto the toasted rolls. Divide the cheese among the rolls. Return to the grill, cheese side up, close the lid, and grill until the other side is toasted and the cheese begins to melt, about 30 seconds more.
Lightly brush the cut side of the rolls with oil, and then grill over high heat until toasted, about 30 seconds. Gently rub the garlic onto the toasted rolls. Divide the cheese among the rolls. Return to the grill, cheese side up, close the lid, and grill until the other side is toasted and the cheese begins to melt, about 30 seconds more.
Build the sandwiches on the buns with meat and vegetables. Serve warm.
