Cut the mushrooms into 1/4-inch (5mm) slices, finely cut garlic, and parsley.
Heat 1 tablespoon of oil in a large frying pan over high heat, when hot add the mushrooms in an even layer. Don't stir for a minute letting the mushrooms brown, then cook, stirring, for a couple of minutes until the mushrooms are soft.
Reduce the heat to low and add the garlic and herbs, cook for 30 seconds.
Take the pan off the heat, add the chopped parsley, and season the mushrooms with salt and pepper.
If your chicken breasts come with tenderloins attached, remove them and use in another dish (or just pan fry them and serve with the stuffed chicken).
Cut a slit horizontally in the chicken breast, creating a pocket (don't cut the breast all the way through, see photos in the post for reference).
Fill the pockets with mushrooms and 2/3 of the grated cheese. If you have some mushrooms left, reserve them - you can add them later to the sauce. Close the pockets with toothpicks (optional).
Heat the remaining 1 tablespoon of oil in a large pan over high heat. When hot add the stuffed chicken and cook on both sides until browned (the chicken doesn't have to be cooked through at this point, only browned). Transfer chicken to a plate.