If using whole steak, freeze for 20 minutes for easier thin slicing, then slice across the grain into very thin strips. Season lightly with salt and pepper.

Heat butter and oil in a large skillet over medium-high heat. Add onions and cook, stirring occasionally, until softened and starting to caramelize, 8–10 minutes. Add peppers and cook 3–4 minutes until tender. Stir in garlic and cook 30 seconds until fragrant. Move veggies to one side of the pan.

Increase heat to high. Add steak in a single layer and sear quickly, stirring to separate the strips. If your pan is small, cook steak in batches so it browns instead of steams. Remove excess juices if the pan becomes too wet.

Return vegetables to the center of the pan. Pour in beef broth, ketchup, Worcestershire, Dijon, and smoked paprika. Bring to a simmer and cook 2–3 minutes until slightly thickened and glossy. Taste and adjust seasoning.

Reduce heat to low. Pile the steak mixture onto the rolls, top each with 1–2 slices of provolone, cover the pan or place under a broiler briefly until cheese is melted and bubbly.

Sprinkle with chopped parsley if desired and serve immediately while hot and gooey.