Place the steak in the freezer for about 1 hour so that it is easy to slice thinly. Once the ribeye is firm slice it into very thin strips, about 1/8-inch thick.
In a small saucepan, melt the butter over medium heat. Add the garlic and parsley and stir. Brush the tops of the rolls with garlic butter and set aside.
Heat the olive oil in a large non-stick skillet. Add the mushrooms and bell pepper and sauté until golden. Transfer the veggies to a medium mixing bowl and set aside.
Add the sliced ribeye to the same skillet and sear until browned on the edges and cooked through. Add the steak to the same bowl as the peppers and mushrooms and toss to combine.
Place the bottom half of the rolls on a parchment paper-lined baking sheet. Using tongs, divide the steak and veggie mixture between the roll bottoms. Top generously with shredded provolone.
Broil for 4-5 minutes in the oven to melt the cheese. (Keep an eye on them! You don't want the rolls to burn.) Remove the sliders from the oven, place the tops on the rolls, and serve warm.