1. Dissolve sugar and 1/2 cup table salt in 2 quarts water in large container; add pork chops and refrigerate 30 minutes. Remove chops from brine; thoroughly pat dry with paper towels, season with 3/4 teaspoon pepper, and set aside.

2. Adjust oven rack to middle position; heat oven to 400°F. Heat oil in heavy-bottomed ovensafe 12-inch nonreactive skillet over medium-high heat until oil begins to smoke; swirl skillet to coat with oil. Place chops in skillet; cook until well browned, 3 to 4 minutes, using spoon or spatula to press down on center of chops to aid in browning. Using tongs, flip chops and brown lightly on second side, about 1 minute. Transfer chops to large plate; set aside.

3. Set skillet over medium-high heat. Add onion and cook, stirring occasionally, until just beginning to soften, about 2 minutes. Add peppers, anchovies, and rosemary; cook, stirring frequently, until peppers just begin to soften, about 4 minutes. Add garlic; cook, stirring constantly, until fragrant, about 30 seconds. Add water and 1/2 cup vinegar and bring to boil, scraping up browned bits with wooden spoon. Reduce heat to medium; simmer until liquid is reduced to about 1/3 cup, 6 to 8 minutes. Off heat, discard rosemary.

4. Return pork chops, browned side up, to skillet; nestle chops in peppers, but do not cover chops with peppers. Add any accumulated juices to skillet; set skillet in oven and cook until center of chops registers 135 to 140°F on instant-read thermometer, 8 to 12 minutes (begin checking temperature after 6 minutes). Using potholders, carefully remove skillet from oven (handle will be very hot) and cover skillet with lid or foil; let stand until center of chops registers 145 to 150°F on instant-read thermometer, 5 to 7 minutes. Transfer chops to platter or individual plates. Swirl butter into sauce and peppers in skillet; stir in optional 2 tablespoons vinegar, if using, and parsley. Adjust seasonings with salt and pepper, then pour or spoon sauce and peppers over chops. Serve immediately.

Serves 4