Combine the potatoes, parsnips, and vegetable bouillon base in a large pot with enough water to just cover the vegetables; season with the sea salt and black pepper. Bring the water to a boil over medium-high heat, and cook until the potatoes and parsnips are tender, 15 to 20 minutes.
Pour the mixture into a blender, filling the pitcher no more than halfway. Hold the lid of the blender closed with a folded towel and carefully start the blender, using a few quick pulses to get the mixture moving before leaving it on to puree. Process in batches until all vegetables are pureed.
Return blended vegetables to the pot, and place over medium heat. Stir the applesauce, balsamic vinegar, garlic paste, and truffle oil into the soup; bring to a simmer, and reduce heat. Simmer until the flavors combine, about 50 minutes. Add the cabbage to the soup, and cook until the cabbage softens, about 10 minutes.