Preheat oven to 375°F. Preheat cast-iron skillet over high heat.
Remove chops from brine, pat dry, and season with pepper.
Add ghee to skillet. Once melted ghee is hot, add pork chops and sear for 2 minutes per side. Add butter, shallots and rosemary, then baste for 1 minute.
Place skillet with chops in oven for 8-10 minutes, or until meat thermometer inserted into thickest part reads 145°F.