Remove pork chops from fridge 30-45 minutes before cooking time.
Use a paper towel to pat dry both sides, and generously salt both sides with coarse pepper and salt.
Heat a cast iron skillet on medium high heat, add butter (2-3 tablespoons).
Fry pork chops on each side, without disturbing until a nice sear forms (about 3-5 minutes per side), leaving at least a half inch of room in between. If necessary, do this in batches.
Remove pork chops once they've reached an internal temperature of 143-145 degrees Fahrenheit for medium, and set on a plate.
Add sliced mushrooms (1 cup), sauté until edges are crisp and browned. Remove the sautéed mushrooms from the skillet and set aside on a plate.
Add minced garlic (2-3 cloves) and shallot to skillet, sauté until caramelized and translucent.
Sprinkle in flour (3 tablespoons) and and whisk until combined. If necessary, add another tablespoon of butter if it's too dry to mix.
Pour in the wine (½ cup) and stock (2 cups) and add fresh herb sprigs if desired, and simmer on high heat until reduced by half, about 5 minutes.
Once reduced, reduce heat to low and add back the sautéed mushrooms, heavy cream (½ cup), and Parmesan cheese (1 cup), whisk to combine.
Return the pork chops to the sauce, remove from heat and serve.