If using a whole steak, trim it and cut crosswise with the grain into roughly 3-inch sections. Place the pieces on a plate and freeze for about 1 hour until firm but not frozen solid.

Using a sharp knife, shave the steak as thin as possible against the grain on a slight angle. Pile the shaved meat together and chop it coarsely about 10 times. If using pre-sliced meat, chop about 5 times.

Heat a 12-inch cast-iron skillet over medium-high heat for about 5 minutes. Add the oil and heat until just smoking.

Add the meat and diced onion in an even layer. Let cook without stirring for 4 to 6 minutes until well browned on one side. Then stir and continue cooking for another 2 to 4 minutes until the meat is browned and no longer pink.

Stir in the torn provolone pieces, Parmesan if using, salt, and pepper. Cook while stirring constantly for 1 to 2 minutes until the cheese melts and combines with the meat.

Turn off the heat. Divide the mixture into two portions shaped roughly the length of the rolls. Place two whole slices of provolone over each portion. Cover and let the cheese melt for about 1 minute.

Place each roll cut side down over the meat portions. Using a large spatula, scoop underneath and flip the meat into the roll to form the sandwich.

Serve immediately.