Season pork chops with salt and black pepper on both sides.
Heat a 12" skillet over medium-high heat and add cooking oil. Then place 4-6 pork chops in the skillet, depending on size, and sear until well browned on both sides. Then remove the pork and set aside.
Reduce the stovetop to medium heat, add more oil if needed, along with the chopped onion. Saute onions until tender and beginning to brown, then add the minced garlic and cook for an additional minute.
Add the sauerkraut, with its liquid, along with brown sugar, chopped apple, and caraway seeds. Stir well to combine. Then place the pork chops on top of the sauerkraut mixture. Loosely cover the skillet and bring to a simmer. Cook for 15 minutes, or until the pork chops have cooked through.
Once the pork has fully cooked, remove from the heat and serve immediately.
Notes
You can substitute thick-cut pork chops, but you will need to increase the cooking time 5-10 minutes, depending on the thickness.