Stir the balsamic vinegar, tomato sauce, brown sugar, garlic, Worcestershire sauce, Dijon mustard, 1/2 teaspoon salt and 1/2 teaspoon black pepper together in a saucepan over medium-low heat; cook the sauce at a simmer for 20 minutes. Remove from heat and allow to sit for 5 minutes.
Preheat a barbecue for medium heat and lightly oil the grate. Season both sides of the pork chops with salt and black pepper. Brush the chops with the sauce from the saucepan.
Cook the pork chops on the preheated barbecue until the chops are no longer pink in the centre, about 5 minutes per side. Remove from the barbecue then allow to rest for 3 minutes before serving with the remaining sauce on the side.