Season the chops lightly with salt and pepper and dredge in the flour, shaking off the excess.

Put the butter and oil in a 12-inch skillet over medium heat. When hot, add 4 of the pork chops and cook, turning once, until golden on both sides and just cooked through, 4 to 6 minutes total. Transfer the pork to a serving platter and tent with foil. Repeat with the remaining chops, adding another tablespoon of oil to the pan if necessary.

Pour off any fat in the pan, add the wine, and scrape up the browned bits from the bottom of the pan with a wooden spoon. Increase the heat to medium high and boil until the wine is reduced to about 2 tablespoons, 2 to 3 minutes. Stir in the cream, chicken broth, and mustard and boil until reduced to a saucy consistency, about 5 minutes. Season to taste with salt and pepper.

Return the pork and any juices to the pan, turn to coat with the sauce, and then transfer back to the serving platter. Drizzle any sauce remaining in the skillet over the chops and serve.