Heat the vegetable oil in a large Dutch oven over medium-high heat. Add the pork cubes and cook until browned on all sides, about 6 to 8 minutes. Remove the pork to a plate and set aside.
Lower the heat to medium. Add the onion to the pot and cook until it softens, about 4 minutes. Stir in the garlic and caraway seeds and cook for 1 minute more.
Return the browned pork to the pot. Pour in the crushed tomatoes and beef broth. Add the salt and black pepper, then stir to combine.
Bring the mixture to a simmer. Add the shredded cabbage, stir once, and cover the pot. Cook for 45 minutes, stirring a few times, until the pork is tender and the cabbage is soft but not mushy.
Taste and adjust salt if needed. Serve hot.