Cook's Note: *Add any leftovers scraps from other parts of the tenderloin that you like
Remove the beef from the refrigerator 1 hour before cooking.
Preheat a grill pan over high heat.
Lightly pound the chain with a smooth meat mallet until it is even thickness throughout. Toss the meat with 1 teaspoon olive oil and season with salt and pepper. Once the grill pan is hot, place the chain on the pan and cook on both sides until cooked through, approximately 3 to 4 minutes per side. If necessary, cut the chain in half or thirds to fit on the pan. Remove the chain from the grill and wrap in aluminum foil. Allow to rest while the onions are cooking.
Add remaining teaspoon of oil to grill pan and saute the onions on the grill until they are tender and beginning to brown, approximately 7 to 10 minutes.
Slice the beef into small strips and divide evenly among the hoagie rolls. Pour any juice from the meat onto the hoagie as well. Top the meat with the cheese, followed by the onions. Wrap the sandwiches in aluminum foil for 10 minutes and serve.