Prepare the beef: Take your partially frozen steak and slice it as thinly as you can manage, cutting against the grain. You want ribbons of meat, not chunks. Season the strips with the salt, pepper, and smoked paprika. Set them aside while you work on the vegetables.

Sweat the vegetables: Place your skillet over a medium heat and add the butter. Once it melts into a gentle foam, toss in the sliced onion, bell pepper, and mushrooms. Stir them around. You want them to soften slowly, releasing their moisture. After about 8 minutes, they should be translucent and fragrant, with the edges just beginning to brown. Add the minced garlic and stir for another 30 seconds until you can smell it properly.

Remove and rest: Tip the softened vegetables into a bowl and cover them with a plate to keep warm. Do not wash the pan — those browned bits on the bottom are pure flavour.

Sear the steak: Increase the heat under the skillet to high. Add the vegetable oil and watch it shimmer. Spread the seasoned beef strips in a single layer — work in two batches if your pan is crowded. Let them sit for 60 seconds without moving them. You should hear a vigorous sizzle. Flip the strips with your tongs; the underside should be a rich, dark brown. Cook for another 30 seconds. The meat will be tender and slightly pink inside.

Deglaze and combine: Pour the beef stock into the hot pan. It will bubble up instantly. Use your spatula to scrape up all the caramelised bits from the base of the pan. Return the cooked vegetables to the skillet, toss everything together, and let it cook for 1 minute to blend the flavours.

Melt the cheese: Lay the slices of provolone over the top of the meat and vegetable mixture. Reduce the heat to low, cover the pan with a lid, and let it sit for 2 minutes. Peek under the lid — the cheese should be fully melted and bubbling around the edges of the beef.

Toast the rolls and assemble: While the cheese melts, split your hoagie rolls and toast them under the grill or in a dry pan until they are golden and crisp. Spoon the cheesy steak mixture generously into each roll. Serve immediately, while the filling is still hot and the bread is crunchy.