01 - Warm olive oil in a large, heavy-bottomed pot or Dutch oven set over medium heat until it shimmers.
02 - Add the sliced onions and carrots to the pot. Cook for 4 to 5 minutes, stirring occasionally, until the onions have softened and turned translucent.
03 - Stir in the minced garlic and caraway seeds. Continue cooking for about 1 minute until the garlic becomes fragrant.
04 - Place the sliced cabbage into the pot and toss to combine with the aromatics. Cook for 5 minutes, allowing the cabbage to begin wilting down.
05 - Sprinkle the smoked paprika, salt, and black pepper evenly over the vegetables and stir to coat.
06 - Pour in the vegetable broth and apple cider vinegar. Stir well, then cover the pot with a tight-fitting lid. Reduce the heat to low and braise for 30 minutes, stirring occasionally, until the cabbage is completely tender and the flavors have melded together.
07 - Remove from heat and taste for seasoning, adjusting with additional salt, pepper, or vinegar as needed. Serve hot as a side dish or light main.