In a large container, dissolve the sugar and salt in 2 quarts water. Add the pork chops and refrigerate for 30 minutes.
Remove the chops from the brine and thoroughly pat dry with paper towels. Season with 3/4 teaspoon pepper.
Heat the oven to 400°F (200°C) and adjust an oven rack to the middle position.
Heat the oil in an ovensafe, 12-inch, nonreactive skillet over medium-high heat until the oil almost begins to smoke. Tilt the skillet to coat the skillet with the oil.
Place the pork chops in the skillet and cook, using a spoon or spatula to occasionally press down on the center of the chops to aid in browning, until well browned, 3 to 4 minutes.
Using tongs, flip the chops and brown lightly on the second side, about 1 minute. Transfer the chops to a large plate.
Set the skillet over medium-high heat. Add the onion and cook, stirring occasionally, until just beginning to soften, about 2 minutes. Add the sweet peppers, anchovies, and rosemary. Cook, stirring frequently, until the peppers just begin to soften, about 4 minutes. Add the garlic; cook, stirring constantly, until fragrant, about 30 seconds.
Add the water and 1/2 cup vinegar and bring to a boil, scraping up the browned bits with a wooden spoon. Reduce the heat to medium; simmer until the liquid is reduced to about 1/2 cup, 6 to 8 minutes. Take he skillet off the heat and discard the rosemary.
Return the pork chops, browner-side up, to the skillet; nestle the chops in the sweet peppers, but do not cover the chops with the peppers. Add any accumulated juices to the skillet; set the skillet in the oven and cook until the center of the pork chops registers 135°F to 140°F (57°C to 60°C) on an instant-read thermometer, 8 to 12 minutes (begin checking the temperature after 6 minutes).
Using potholders, carefully remove the skillet from the oven (the handle will be very hot) and cover the skillet with a lid or foil; let stand until the center of the chops registers 145 to 150 °F (65°C) on an instant-read thermometer, 5 to 7 minutes.
Transfer the pork chops to a platter or individual plates. Swirl the butter into the sauce and the sweet peppers in the skillet; taste and stir in the optional 2 tablespoons vinegar, if desired, and the parsley. Adjust the seasonings with salt and pepper, then pour or spoon the sauce and peppers over the chops. Serve immediately.