Here is a soup that can be prepared with most any vegetable like broccoli, asparagus, squash, and cauliflower. The potato acts as a thickener. The onion and garlic can be sautéed in a small amount of water rather than oil. This soup is both dairy free and oil free and contains no flour so is also gluten free.
In a stock pot sauté cut up onions, minced garlic, a stalk or two of chopped celery, and a chopped carrot and a diced red potato or two in about 1/4 cup of water. Sauté about 5 minutes on medium temperature until the potato is somewhat softened. Add any chopped vegetable like asparagus, broccoli, cauliflower, or squash and sauté a few minutes more. Add water or vegetable broth to cover by about 2 inches. Bring soup to a boil then lower heat and cook covered until vegetables are tender. Allow to cool and put aside 2 or 3 cups of the cooked vegetables to add to the soup later. Put the rest of the soup into a blender and process until smooth or somewhat chunky. Pour back into the pot along with the chunky vegetables. Heat to serve.