Preheat your griddle to high heat, around 450–500°F, so it’s ripping hot before the steak hits the surface. At the same time, brush the French rolls with melted butter, sprinkle with sesame seeds, and toast in a 350°F oven for about 5 minutes until the exterior is lightly crisp but still soft inside.

Add the diced onion to the hot griddle and sauté for 3–5 minutes, stirring frequently, until softened and lightly caramelized. Move the onions to the cooler side of the griddle once tender.

Place the shaved ribeye onto the hot griddle and season evenly with salt and black pepper. Let it sear for 1–2 minutes, then begin chopping and turning the meat with a spatula until finely broken down and nearly cooked through.

Add the sautéed onions back into the chopped ribeye and mix thoroughly. Form the mixture into equal portions and lay slices of Cooper sharp cheese over each pile, allowing it to melt completely for 1–2 minutes.

Using a spatula, scoop each cheesy steak portion into a toasted roll. Press gently to pack the filling in evenly from end to end.

Wrap each sandwich tightly in foil and let rest for 3–5 minutes to steam and meld the flavors together. Unwrap and serve immediately while hot, juicy, and perfectly melty.