Heat a skillet over medium heat. Sauté the mushrooms until cooked through, adding a tablespoon of water, if needed. Transfer to a bowl and set aside.
Using a sharp knife, cut a pocket along the thin edge of each pork cutlet. Make the pocket almost as large as the cutlet itself, leaving the other three edges connected.
Stuff each pocket with mushrooms and grated cheese until full.
Sprinkle salt and pepper on both sides of the pork. Lay each cutlet in the breadcrumbs to cover both sides.
Heat enough olive oil to cover the surface of a medium cast-iron skillet over medium-high heat. When the oil is hot enough that drips of water sizzle, but before it starts smoking, lay each cutlet in the skillet.
Cook until the bottom side is golden brown, about 2-4 minutes. Flip the over and cook an addition 2-4 minutes until the second side is also golden brown.
Transfer to a plate and cover with a bowl for about 5 minutes.
Serve.
