Use a serrated knife to cut each hoagie roll about three-quarters of the way through, then dice the onion and prepare the thinly sliced ribeye. The roll should remain connected along one side, creating a pocket that holds the filling.

Mix the softened butter and pressed garlic in a small bowl, then spread it over the cut surfaces of the rolls and toast them on a large skillet, flat cooktop, or griddle over medium heat. Remove the rolls when the cut sides are golden and smell buttery and garlicky.

Add 1 Tbsp oil to the cooking surface and cook the diced onion with a light sprinkle of salt, stirring as it softens and turns translucent. Transfer the onion to a bowl once it is golden-amber and sweet smelling.

Raise the heat to high, add 1 Tbsp oil, and arrange the shaved ribeye in an even layer without crowding it. Leave it untouched for a couple of minutes until the underside browns, then turn it, season with the salt and pepper, cook through, and fold in the onions.

Separate the beef mixture into 4 portions, place 2 slices of provolone over each portion, and turn off the heat. The residual heat should soften the cheese over the meat without continuing to cook the ribeye aggressively.

Spread mayonnaise over the toasted side of each roll, set one roll over a portion of cheesy steak, and use a spatula to turn the filling up into the bun. Scrape firmly so the melted cheese and browned bits land inside the roll rather than staying on the skillet.