01 - Heat olive oil over medium heat in a large Dutch oven or deep skillet. Add sliced onion and julienned carrot; sauté for 5 minutes until tender and translucent.
02 - Add minced garlic and cook for 1 minute until fragrant, stirring constantly to prevent burning.
03 - Stir in the thinly sliced cabbage. Cook, tossing occasionally, for about 10 minutes until it begins to wilt and reduce in volume.
04 - Sprinkle in smoked paprika, dried thyme, black pepper, and salt. Toss thoroughly to evenly coat all vegetables with the seasonings.
05 - Pour in vegetable broth and apple cider vinegar. Add the bay leaf and stir to combine, scraping up any browned bits from the bottom of the pot.
06 - Cover the pot, reduce heat to low, and braise for 30 minutes, stirring occasionally, until the cabbage is very tender and the flavors have melded together.
07 - Remove and discard the bay leaf. Taste and adjust seasoning with additional salt and pepper as needed. Serve hot as a side dish or light main course.