Adjust oven racks to the top- and lower-third positions and preheat to 425 degrees F. Put a wire rack in a rimmed baking sheet.
Toss the cabbage, apples, 2 tablespoons of the vinegar, olive oil, 2 teaspoons of the brown sugar, 3/4 teaspoon salt and a few grinds of black pepper together on another baking sheet. Roast on the top rack until the cabbage and apples are golden in spots and tender, 20 to 25 minutes. Remove and toss with dill, if using.
Meanwhile, lay the pork chops between two pieces of plastic wrap and pound until about 1/4 inch thick. Sprinkle all over with 1/2 teaspoon salt and a few grinds of black pepper. Combine 1 tablespoon of the sour cream and 1 teaspoon of the mustard in a small bowl and brush both sides of each chop with the mixture.
Pour the panko crumbs out onto a plate and press each side of the pork chops into the crumbs. Generously spray both sides of each chop with cooking spray and place on the rack on the prepared baking sheet. Bake on the lower rack until the pork chops are golden, crispy and cooked through, 6 to 8 minutes, flipping halfway through.
Mix together the remaining 2 tablespoons of sour cream, 2 teaspoons water and the remaining 1 teaspoon each mustard, brown sugar and vinegar. Divide the pork chops and apple slaw among four plates; drizzle the chops with some of the sauce.
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