Cut the skirt steak into 4-inch sections, season it with 3/4 teaspoon salt and the black pepper, and let it stand for 10 minutes.
Heat half the oil in a large skillet over medium-high heat and cook the mushrooms with the remaining salt for 7 to 9 minutes until browned and dry.
Stir the Worcestershire into the mushrooms for 30 seconds and transfer them to a plate.
Add the remaining oil and sear the skirt steak for 2 to 3 minutes per side until it reaches 145°F.
Rest the steak for at least 3 minutes, slice it thinly across the grain and combine it with the mushrooms.
Divide the filling among the rolls, add two Swiss slices to each and broil for 1 to 2 minutes until melted.
