Prep the steak. Lay the skirt steak on a cutting board and place a sheet of plastic wrap over it. Pound with the smooth side of a meat tenderizer or a rolling pin to thin it to a thickness of about 1/4-inch. Cut the slab into 3 or 4 pieces. Lightly season both sides with salt and freshly ground black pepper.

Sear the meat. Heat 1 tablespoon of oil in a large skillet over medium-high heat, then add 2 of the steak pieces. Cook for about 5 to 6 minutes, turning halfway through. It should be medium-rare. Repeat with the other 1 or 2 pieces. Set aside to rest for at least 5 minutes.

Cook the mushrooms. Wipe out the pan lightly and add another 1 tablespoon of oil. Add the mushrooms to the pan and cook over medium heat for about 3 to 4 minutes, until browned.

Slice the beef and add the onions and peppers. While the mushrooms cook, slice the meat thinly. Remove the cooked mushrooms to a plate or platter and add another tablespoon of oil to the pan. Add the sliced onion and peppers to the pan and season lightly with salt and pepper; cook over medium-high heat for about 4 to 6 minutes, or until softened and lightly charred in places.

Broil to melt the cheese. Position the rack in the upper third of the oven and preheat the broiler. Add the steak strips and mushrooms back to the pan and toss to blend. Top with the provolone and mozzarella cheese and place the pan under the broiler and cook for 2 minutes, or until the cheese is melted and beginning to brown.