1. Season the thinly sliced steak with kosher salt, black pepper, garlic powder, and Worcestershire sauce, tossing to coat evenly.

2. In a large skillet over medium heat, add the olive oil and butter, then stir in the sliced onion with a pinch of salt. Cook until the onions are soft, lightly golden, and sweet, about 8–10 minutes.

3. Push the onions to one side of the pan or transfer them to a plate. Increase the heat to medium-high and add the seasoned steak in a single layer. Sear just until browned on the outside and still tender, 3–4 minutes.

4. Return the onions to the center of the pan with the steak. Add the beef broth or water, scraping up any browned bits from the bottom, and toss everything together. Turn off the heat and set the mixture aside.

5. In a small bowl, stir together the mayonnaise and Dijon mustard, if using, to make a tangy sandwich spread.

6. Lay out the slices of bread. Butter one side of each slice. On the unbuttered side of four slices, layer one slice of provolone, a generous portion of the warm steak-and-onion mixture, a handful of shredded mozzarella or Monterey Jack, and a second slice of provolone.

7. Spread a thin layer of the mayo-Dijon mixture on the unbuttered side of the remaining bread slices if desired, then place them on top of the sandwiches, buttered side facing out.

8. Heat a clean skillet or griddle over medium-low heat. Place the sandwiches in the pan and cook until the bottom is deep golden and crisp and the cheese is beginning to melt, about 3–4 minutes.

9. Flip each sandwich carefully and cook the second side until the bread is golden brown and the cheese is fully melted, another 3–4 minutes, adjusting the heat as needed so the bread doesn’t burn.

10. Transfer the sandwiches to a cutting board and let them rest for 1 minute, then slice in half or into quarters and serve hot while the cheese is still gooey and melty.