Preheat oven to 425°.
In a 12-inch cast-iron skillet, melt 4 tablespoons butter over medium heat. Add onion; cook until tender, 2 to 3 minutes. In a medium bowl, stir together onion, crumbled cornbread, broth, and herbs.
Cut a pocket into each pork chop by cutting into side of chop toward the bone. Stuff cornbread mixture into chops. Sprinkle salt and pepper all over pork chops.
In same skillet, heat oil over medium-high heat. Add pork chops; cook until browned, 2 to 3 minutes per side. Transfer skillet to oven.
Bake for 20 minutes. Remove pork chops from skillet; keep warm.
Stir wine into skillet; cook over medium heat for 2 to 3 minutes, scraping browned bits from bottom of skillet with a wooden spoon. Whisk in cream, mustard, sage sprig, and remaining 2 tablespoons butter; cook, whisking constantly, until thickened, 2 to 3 minutes. Return pork chops to skillet; cook until heated through. Garnish with sage, if desired.