Place the pork chops between 2 pieces of plastic wrap and pound with a mallet or heavy skillet until 1/4-inch-thick.
Sprinkle the pork on both sides with salt and pepper. Put the flour in a shallow dish and dredge the pork in it, shaking off any excess.
Heat the olive oil and 2 tablespoons butter in a large skillet over medium-high heat. Add half of the pork and cook until browned and cooked through, 2 to 3 minutes per side. Remove to a plate and set aside. Repeat with the remaining pork.
Add the mushrooms to the skillet and stir. Cook until golden brown, 5 to 6 minutes.
Pour in the Marsala and beef broth and stir to deglaze the pan, scraping up the browned bits. Cook until the liquid is reduced by half, 5 to 6 minutes. (If the liquid reduces too quickly, splash in more broth as needed.)
Whisk the cornstarch into the heavy cream in a small bowl. Pour into the sauce mixture and let it bubble and thicken for another minute.
Turn off the heat and stir in the remaining 2 tablespoons butter. Serve the pork with the Buttered Noodles and spoon some of the mushrooms and Marsala sauce on top. Sprinkle with the parsley.
Buttered Egg Noodles:
Add the egg noodles to a pan of salted boiling water and cook according to the package directions, 6 to 7 minutes.
Drain, put back in the pan and add the butter, then season with salt and pepper. Add the parsley and toss.