Preheat the oven to 350°F. Lightly grease a 9x13-inch baking dish or line it with parchment paper.
Without separating the rolls, slice the whole slab of rolls in half horizontally. Place the bottom half into the prepared baking dish.
Layer the provolone cheese over the bottom rolls. Add the roast beef in an even layer, then top with the white cheddar, Swiss, or remaining provolone. Place the top half of the rolls over the cheese.
In a small bowl, stir together the melted butter, garlic, Worcestershire sauce, Dijon mustard, dried parsley, black pepper, salt, and parmesan if using.
Brush the garlic butter mixture generously over the tops of the rolls. Cover the baking dish with foil and bake for 15 minutes.
Remove the foil and bake for another 7–10 minutes, or until the tops are golden and the cheese is melted.
While the sliders bake, make the au jus. In a small saucepan, melt the butter over medium heat. Add the garlic and cook for about 30 seconds, just until fragrant.
Stir in the beef broth, Worcestershire sauce, Dijon mustard, soy sauce, thyme, and black pepper. Bring to a gentle simmer and let it cook for 8–10 minutes so the flavors can come together.
If you want the au jus to have a little more body, stir in the cornstarch slurry and simmer for 1–2 more minutes. Keep it thin enough for dipping.
Sprinkle the baked sliders with fresh parsley, slice, and serve warm with the homemade au jus on the side.