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Stir 1 ¼ teaspoons paprika, ¾ teaspoon kosher salt, and ½ 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 or frying pan 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 the 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, ¼ 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.