Slice beef with the grain into 1-inch pieces. Arrange in a single layer between two sheets of plastic wrap or wax paper and pound until paper thin.
In a large skillet over medium-high heat, heat 2 teaspoons oil until shimmering. Add onions and cook until softened, about 5 minutes. Transfer to small bowl.
Add 2 teaspoons to the same skillet and heat over high heat until smoking. Add half of beef to skillet (slices may overlap), season with salt and pepper, and cook until meat is browned, about 1 minute per side.
Remove from heat and layer 8 pieces of provolone over beef. Using spatula, pick up half of beef-provolone mixture. Cover skillet until provolone is melted, about 1 minute.
Divide beef-provolone mixture evenly between 2 rolls, evenly distribute half of the onions over sandwiches, and pour any accumulated juices from skillet onto meat. Wrap each sandwich tightly in aluminum foil and set aside.
Repeat with remaining 2 teaspoons oil, remaining half of beef, remaining 8 pieces of provolone, remaining 2 rolls, and remaining half of onions. Wrap each sandwich tightly in foul and let sit for about 1 minute. Serve with roasted red peppers if desired.