Prepare the beef. Slice the partially frozen beef as thinly as possible against the grain — you're aiming for strips about 3–5mm thick. The meat should feel firm but slice easily, and you'll hear a clean, quiet slicing sound as the knife moves through. Set the strips aside on a plate.

Sauté the vegetables. Heat 1 tablespoon of olive oil in a large skillet or griddle over medium-high heat. Add the sliced onions and bell peppers. Cook for 5–7 minutes, stirring occasionally, until they are soft and beginning to brown at the edges. You'll know they're ready when the onions turn translucent and you smell that sweet, caramelised aroma. Transfer the vegetables to a bowl and set aside.

Cook the beef. Increase the heat to high and add the remaining 1 tablespoon of olive oil to the same pan. Spread the beef strips in a single layer — don't overcrowd the pan, or they'll steam rather than sear. Cook for 2–3 minutes without moving them, until the underside is deeply browned and you hear a vigorous sizzle. Flip the strips and cook for another 1–2 minutes. The beef should be browned on the outside but still tender, with a rich, savoury smell filling your kitchen. If using, pour in the beef broth at this stage and let it bubble for 30 seconds to create a light jus.

Combine and season. Return the cooked peppers and onions to the pan with the beef. Add the minced garlic, salt, pepper, and dried oregano. Toss everything together for about 1 minute, until the garlic is fragrant and the mixture is piping hot. You'll see the steam rising and the colours melding beautifully.

Melt the cheese. Reduce the heat to low. Divide the beef and vegetable mixture into four even piles in the pan. Lay 2 slices of provolone cheese over each pile. Cover the pan with a lid or a sheet of aluminium foil for 1–2 minutes, until the cheese is completely melted and gooey. You'll see the edges of the cheese turn glossy and soft.

Toast the rolls. While the cheese melts, spread the cut sides of the hoagie rolls with the softened butter. Place them on a separate griddle or under the grill for 1–2 minutes, until golden brown and crisp. The rolls should feel firm to the touch and smell nutty and warm.

Assemble and serve. Using a spatula, lift each cheesy beef pile and place it directly onto the bottom half of a toasted roll. Close the sandwich with the top half. Slice in half on a diagonal if you like, and serve immediately while the cheese is still stretchy and the roll is crisp.