Adjust the oven racks to the top and lower-third positions and preheat the oven to 425 degrees F. Put a wire rack in a rimmed baking sheet.
Lay the pork chops between two pieces of plastic wrap and pound to about 1/4 inch thick. Sprinkle all over with 1/2 teaspoon salt and a few grinds of 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.
Mix the panko and parsley together on 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 in the prepared baking sheet. Bake on the lower rack, flipping halfway through, until the pork chops are golden, crispy and cooked through, 6 to 8 minutes.
Mix the brown sugar and vinegar with 2 teaspoons water and the remaining 2 tablespoons sour cream and remaining 1 teaspoon mustard in a small bowl. Serve the pork chops with the sauce and the green salad.
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