Prep. Thinly slice the bell pepper and onion. Finely mince the garlic.
Bring the griddle grill to medium-high heat. Melt butter on the griddle and toast the cut sides of the sandwich buns until they turn a light golden brown. Set aside on a serving platter.
Fire up. Oil the griddle grill and turn the heat up to high. Begin to sauté the peppers, onions, and garlic.
Cook. Begin to sauté the peppers, onions, and garlic.
Spread the ribeye roast out on the griddle grill, and as liquid begins to release from the meat, season with salt and pepper, and use two heavy-duty spatulas to chop the meat on the griddle into shreds.
As the sautéed peppers and onions become wilted and translucent, the shredded meat should be turning from raw to almost cooked. Mix the meat with the peppers and onions and continue to cook until the meat is just cooked through.
Divide the meat into two loose piles that will fit under a grill lid. Add 4 slices of the cheese to each pile of meat. Add a squirt of water around the meat and cover. Allow it to cook for 2 to 3 minutes, until the cheese is melted and gooey.
Serve. Using both spatulas, scoop up the cheesesteak filling and scrape it on to the bun. Serve with plenty of napkins.
