Preheat oven to 425F. While the oven is preheating, chop the vegetables. Remove the stem and leaves from the cauliflower and chop into florets. Dice the shallot, carrot, celery, and garlic. Whisk together the tahini marinade.
Toss the cauliflower florets in the tahini marinade and spread out onto a baking sheet. Roast for 20 minutes, stirring the pan halfway through cooking time.
Meanwhile, heat a tablespoon of oil in a large soup pot over medium heat. Once warm add the shallot and cook for 2 minutes. Then add the carrot, celery, garlic, salt, and pepper and stir well. Cook for 5 minutes. After 5 minutes add a splash of broth and stir. Turn the heat to low until the cauliflower is done roasting.
When the cauliflower is done, remove from the oven but leave it on at 425F, add to the soup, along with the remaining broth, beans, nutritional yeast, and herbs. Simmer for 15-20 minutes uncovered.
While the soup is simmering, go ahead and get started on the croutons. Cube the sourdough and toss with olive oil, salt, and pepper. Add everything from the basil to the salt and pepper to a high speed blender to prepare the pesto. Drizzle the pesto over top of the bread. Bake in the oven for 10 minutes.
Rinse out the blender, and when the soup is done simmering, turn off the heat, remove the herbs, and transfer the soup with a ladle to the blender. Place a kitchen towel over the lid of the blender and blend on high until smooth all the way through. Transfer back to the soup pot and stir in the red wine vinegar. Serve immediately with the croutons and minced parsley for garnish.