In a Dutch oven (5-quart pot with a tight-fitting lid), heat 1 tablespoon oil over medium-high. Generously sprinkle pork with salt and pepper. Cook until golden brown, about 3 minutes per side. Remove pork.
Reduce heat to medium-low. Add remaining tablespoon oil, onion, coleslaw mix, and garlic; season with salt and pepper. Cook, stirring frequently, until cabbage has wilted, about 10 minutes.
Raise heat to high. Add vinegar, caraway seeds, and 1 1/4 cups water; bring to a boil. Add potatoes, and reduce heat to a simmer. Cover, and cook until cabbage and potatoes are almost tender, about 20 minutes.
Return pork to pot; cover, and continue cooking until pork is just cooked through and potatoes are tender, 10 to 15 minutes more.
Caraway seeds, which are common in rye bread, have a nutty, licorice-like flavor that pairs well with cabbage.