Stir 1 1/4 teaspoons paprika, 3/4 teaspoon kosher salt, and 1/2 teaspoon black pepper together in a small bowl. Pat 4 bone-in pork chops dry with paper towels, then season all over with the spice mixture.

Melt 1 tablespoon of the unsalted butter in a large skillet over medium-high heat. Add 2 of the pork chops and cook until well browned and an internal temperature of at least 145°F, 4 to 5 minutes per side. Transfer to a plate. Add 1 tablespoon of unsalted butter to the pan and repeat browning the remaining 2 pork chops and transferring to the plate.

Reduce the heat to low. Add the remaining 2 tablespoons unsalted butter, 2 fresh rosemary sprigs, 1/4 cup packed brown sugar, 2 tablespoons water, 2 tablespoons soy sauce, and any accumulated juices on the pork chop plate. Cook, stirring occasionally, until the butter melts and the sauce thickens slightly, about 1 minute.

Serve the pork chops with the sauce spooned over the top, garnished with more fresh rosemary leaves if desired.