Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Brush pork chops with 2 teaspoons white vinegar and sprinkle with 1/4 teaspoon dill, 1/4 teaspoon pickling spice, salt, and black pepper. Place pork chops in a broiling pan.
Broil in the preheated oven until juices run clear and chops are browned, 4 to 8 minutes per side. Drizzle chops with 1 more teaspoon vinegar and flip chops halfway through cooking. An instant-read meat thermometer inserted into the thickest part of a chop should read at least 145 degrees F (65 degrees C).
Place beef broth, potatoes, and 1/4 cup white vinegar in a saucepan, bring to a boil, cover, and boil for 4 minutes. Stir in 1/4 teaspoon dill, 1/4 teaspoon pickling spice, and shredded cabbage; cover and boil for 4 more minutes. Drain liquid and stir 2 tablespoons vinegar into cabbage mixture. Season with salt and black pepper and serve with broiled pork chops.
You could marinate the pork chops with some vinegar before cooking if you want them a little more tangy. If you like larger chunks for your potatoes, you might need to boil them a little longer.