Season pork chops on both sides with salt and pepper. Dredge in flour, shaking off excess.
Heat half of the butter and oil in a large skillet over medium-high heat until foaming subsides. Cook pork chops for 3-4 minutes per side, until browned (should read 145 degrees F with a meat thermometer). Very thin chops might need as little as 2 minutes per side.
Transfer pork chops to a plate and cover with foil to keep warm.
Add shallots, garlic, and mushrooms to pan and sauté until mushrooms are soft and beginning to brown, about 5 minutes.
Stir 2 tablespoons flour into the mushroom mixture and cook for 1 minute.
Add half of the marsala wine and cook for an additional 1-2 minutes, scraping any brown bits from the bottom of the pan.
Next, add chicken broth and bring to a boil.
Add the remaining half of butter and marsala wine to pan then lower heat and simmer for 5-8 minutes, until sauce is slightly thickened.
Add pork chops back to the pan and simmer for 1-2 minutes.
Transfer pork chops to a platter and spoon sauce over the top.
Serve warm with mashed potatoes, rice, or pasta.
ENJOY!