Slice the Steak: Using a sharp knife, slice the ribeye as thinly as possible against the grain.
For the filling, heat a little vegetable oil on a large hot plate or heavy frying pan over a medium-high heat. Add the onions and peppers, cooking until they are soft and slightly charred. Push the vegetables to one side, then add the sliced steak to the hot surface. Season with salt, pepper, and Worcestershire sauce. Cook the beef quickly until browned, then mix everything together.
Divide the steak and vegetable mixture into two portions, about enough to fit the length of your rolls. Place 3 slices of Provolone / Emmental cheese on top of each portion and leave for a minute until the cheese is melted, sticky, and covers the beef.
To assemble the sandwiches: Spread garlic butter inside the hoagie rolls and toast them until golden. Using a spatula, scoop the cheesy steak mixture straight into the rolls and serve immediately.