FOR THE ROAST: Using sharp knife, cut slits 1 inch apart in crosshatch pattern in fat cap of roast, being careful not to cut into meat. Combine salt and brown sugar in medium bowl. Rub salt mixture over entire pork shoulder and into slits. Wrap roast tightly in double layer of plastic wrap, place on rimmed baking sheet, and refrigerate at least 12 and up to 24 hours.
Adjust oven rack to lowest position and heat oven to 325 degrees. Unwrap roast and brush off any excess salt mixture from surface. Season roast with pepper. Transfer roast to V-rack coated with nonstick cooking spray set in large roasting pan and add 1 quart water to roasting pan. (Monitor during cooking and add more water if needed to keep fond from burning.).
Cook roast, basting twice during cooking, until meat is extremely tender and instant-read thermometer inserted into roast near but not touching bone registers 190 degrees, 5 to 6 hours. Transfer roast to carving board and let rest, loosely tented with foil, 1 hour. Transfer liquid in roasting pan to fat separator and let stand 5 minutes. Pour off 1/4 cup jus; discard fat and reserve remaining jus for another use.
FOR THE SAUCE: Bring peaches, wine, granulated sugar, 1/4 cup vinegar, 1/4 cup defatted jus, and thyme to simmer in small saucepan; cook, stirring occasionally, until reduced to 2 cups, about 30 minutes. Stir in remaining tablespoon vinegar and mustard. Remove thyme, cover, and keep warm.
Using sharp paring knife, cut around inverted T-shaped bone until it can be pulled free from roast (use clean kitchen towel to grasp bone). Using serrated knife, slice roast. Serve, passing sauce separately.