In a heavy skillet fitted with a lid, heat 3 tablespoons of the oil over medium-high heat. Brown the chops in the hot oil, cooking 2 or 3 at a time. Cook for about 3 minutes on each side until nicely brown. Transfer to a plate, season lightly with salt and pepper, and cover with foil to keep warm.
Pour the fat from the pan and wipe it clean with a paper towel. Heat the remaining 3 tablespoons of oil in the pan. Cook the scallions for about 2 minutes, stirring, until softened. Add the garlic and cook for 30 to 40 seconds longer, just until fragrant. Add the wine, mustard, and herbs and cook, stirring, for 2 to 3 minutes until well mixed.
Return the chops to the skillet and turn them once or twice to coat with the pan juices. Cover and cook over medium heat for about 15 minutes or until an instant-read thermometer inserted in a thick, meaty chop registers 140°F for medium-rare meat. Baste the meat several times during cooking.
Transfer the chops to a platter and cover to keep warm. Put the cream in the hot skillet and stir for a few moments to heat it. Pour the broth and cream into the skillet and cook, stirring constantly, for about 5 minutes until the sauce thickens, reduces slightly, and is heated through. Taste for seasoning and add more salt and pepper, if needed.
Pour the sauce over the chops and serve immediately.