Heat a large skillet on medium-high heat; add the butter and olive oil to the pan.
Next, add the sliced mushrooms. Season the mushrooms with a pinch of salt and pepper then sauté 5 to 6 minutes until tender and caramelized in color. Slide the mushrooms off to the slide of the pan.
Liberally season both sides of the pork chops with kosher salt and cracked black pepper and place in the hot skillet. Adjust heat to medium-low if needed; sear the pork chops on the first side until you see the cook line about three quarters up the side of the pork chop (this will take around 15 minutes for thick chops), then turn and finish cooking through (about 5 minutes more.
The internal temperature of the pork chops should be 145°F or higher for safe consumption according to the latest food safety standards.
Transfer the pork chops and mushrooms to a plate and allow to rest for five minutes.
Optional: deglaze the pan by adding ¼ cup of chicken broth to the hot skillet. Use a spatula or wooden spoon to scrape the browned bits from the bottom of the pan. Next, add a splash of heavy cream (about a tablespoon) to the pan and allow the sauce to reduce and thicken slightly, which will take a minute or two.
Serve the pork chops covered with sautéed mushrooms and spoon over the pan sauce, if using, and garnish with parsley if desired.