01 - Heat olive oil in a large, heavy-bottomed pot or Dutch oven over medium heat until the oil shimmers.
02 - Add the sliced onions and carrots to the pot; sauté for 4 to 5 minutes, stirring occasionally, until the onions are softened and translucent.
03 - Stir in the minced garlic and caraway seeds; cook for about 1 minute until fragrant, taking care not to let the garlic brown.
04 - Add the sliced cabbage to the pot and toss everything to combine. Cook for approximately 5 minutes, turning occasionally, until the cabbage begins to wilt and reduce in volume.
05 - Sprinkle the smoked paprika, salt, and freshly ground black pepper evenly over the vegetables and stir to distribute the seasonings throughout.
06 - Pour in the vegetable broth and apple cider vinegar, stirring gently to scrape up any browned bits from the bottom of the pot.
07 - Cover the pot, reduce the heat to low, and braise for 30 minutes, stirring every 10 minutes, until the cabbage is completely tender and the flavors have melded together.
08 - Taste the braised cabbage and adjust the salt, pepper, or vinegar as needed. Transfer to a warm serving dish and serve hot.