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.