Begin by dicing the onion into small, even pieces. In a skillet over medium heat, sauté the diced onion in a splash of oil until it turns translucent and fragrant, about 5 minutes.
Transfer the sautéed onions to your slow cooker. Add the sliced carrots and chopped cabbage, distributing them evenly.
Pour the vegetable broth over the vegetables, covering most of them. Stir in the tomato paste along with smoked paprika and black pepper, mixing well to combine.
Set your slow cooker to low and cook for 6 to 8 hours. During this time, the vegetables will soften, releasing sweet and earthy aromas, and the broth will develop a smoky, savory flavor.
Once the cooking time is up, taste the soup and add salt gradually until the flavor is balanced and savory. If desired, remove the lid during the last 30 minutes to allow excess liquid to reduce slightly for a thicker texture.
Turn off the slow cooker and let the soup sit for about 10 minutes to allow flavors to meld. Then, give it a gentle stir and ladle into bowls.
Enjoy the comforting richness of this soup, perhaps with a slice of crusty bread or a drizzle of olive oil. The tender, velvety cabbage and sweet carrots make each spoonful satisfying and warm.