Stir the balsamic vinegar, ketchup, 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 an outdoor grill 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 grill until the pork is no longer pink in the center, about 5 minutes per side. An instant-read thermometer inserted into the center should read 145 degrees F (63 degrees C). Remove from the grill and allow to rest for 3 minutes before serving with the remaining sauce on the side.