Place the thinly shaved ribeye in a bowl. Add 2 tbs olive oil, 1 tbs Worcestershire, minced garlic, 1 tsp kosher salt and 1 tsp black pepper. Toss to coat evenly and let sit at room temperature for 15 minutes (or refrigerate up to 2 hours).

Cook steak

Heat a large cast-iron skillet or flat-top griddle over high heat until very hot. Add the marinated steak in an even layer (work in batches to avoid steaming). Sear the shaved ribeye for 1-2 minutes, tossing once, until just browned but still juicy. Remove to a warm plate and reserve any pan juices for the beef jus. Keep warm.

Grilled Onions

While the steak rests, wipe the skillet if it has burned bits, then add 1 tbs olive oil and 1 tbs butter over medium heat. Add the thinly sliced onion, 1 tsp salt and 1 tsp brown sugar (if using). Cook, stirring occasionally, until the onions are softened and deeply browned, about 10–12 minutes. Remove from heat and keep warm.

Beef Jus (Dipping Sauce)

In a small saucepan, combine 2 cups beef stock, reserved beef drippings (or 2 tbs beef concentrate), 1 tbs dry red wine (if using), 1 tsp Worcestershire, and 1 tsp garlic powder. Bring to a gentle simmer over medium heat.

Simmer until slightly reduced and flavorful, about 8–10 minutes. Taste and adjust seasoning with 1 tsp salt and 1 tsp black pepper. Whisk in 1 tbs unsalted butter off heat to add richness and a glossy finish. Keep warm in a small serving bowl for dipping.

Assembly & Cheese

Butter the cut sides of the rolls with the 2 tsp butter. Heat a clean skillet or griddle over medium-high heat and toast the rolls, buttered side down, until golden, about 1–2 minutes.

Divide the cooked shaved ribeye evenly among the three rolls. Top each with a generous portion of grilled onions. Layer provolone slices over the steak and onions.

Place the assembled sandwiches back on the skillet or under a broiler for 1–2 minutes, just until the provolone melts and becomes slightly gooey. Remove immediately.

Serve each sandwich with a small bowl of warm beef jus on the side for dipping. Garnish jus with chopped parsley if desired.