Place the thinly sliced ribeye in a bowl. Add soy sauce, Worcestershire sauce, 1 tablespoon olive oil, minced garlic, black pepper and cornstarch. Toss to coat evenly. Let marinate at room temperature for 10–15 minutes (or refrigerate up to 1 hour).

Cook steak

Heat a large skillet or cast-iron pan over high heat until very hot. Add the marinated steak in a single layer (work in batches if necessary) and sear, stirring occasionally, for about 2–3 minutes until just browned and mostly cooked through. Remove steak to a bowl and set aside.

Vegetables & Toppings

Slice vegetables

While steak marinates, thinly slice the onion and core and thinly slice the green bell pepper into strips.

Caramelize onions and peppers

Wipe the skillet if needed, reduce heat to medium, add 1 tablespoon butter and a drizzle of oil. Add the sliced onions and peppers, sprinkle with 1 teaspoon salt and 1/2 teaspoon black pepper, and cook, stirring occasionally, for 8–12 minutes until softened and caramelized. Transfer vegetables to the bowl with the cooked steak and mix to combine.

Bread & Cheese

Prepare rolls

Preheat the oven broiler or set an oven to 400°F (200°C). Split the hoagie rolls and brush the cut sides with 1 tablespoon olive oil or spread lightly with butter. If using broiler, place rolls cut-side up on a baking sheet and toast 1–2 minutes until lightly golden; if oven, toast 4–5 minutes.

Assemble and melt cheese

Divide the steak and vegetable mixture evenly among the 4 rolls, piling into the bottom halves. Top each with two slices of provolone. Place assembled sandwiches under the broiler or back in the oven for 1–3 minutes until the cheese is melted and bubbling.

Finishing

If desired, spread mayonnaise on the top halves of the toasted rolls. Close each sandwich and press lightly. Serve immediately while hot.