Tip: Use a medium-size pot if preparing the basic recipe. Use a larger stock pot if including extra vegetables or other add-ins.
Heat the oil or butter over medium-high heat and sauté the onion, if using (and/or the optional celery or leeks) until soft, about 3-5 minutes.
Add the cauliflower, broth. and optional add-ins (see notes). Start with 3-3½ cups of broth if using a smaller pot. If using a larger stock pot, start with 4 cups. Bring to a boil.
Lower the heat and simmer with a tight-fitting lid (this also helps decrease the cruciferous odor if anyone in the household is sensitive to it) for about 20 minutes or until the cauliflower is fork tender.
Use an immersion blender to puree soup. If you don’t have an immersion blender, you can pour contents from pot into a standing blender. (In this case, vent the lid, cover with a tea towel, and be careful of the hot liquid.) Fee free to leave the soup chunky if you prefer, but pureeing it really adds to the thicker texture of the soup.
At this point, you may add more broth, half a cup at a time, if you prefer a thinner soup. If the soup seems too thin, you can simmer it with the lid off, stirring regularly. Add the salt, starting with ½ teaspoon, and some cracked black pepper. Continue to taste for seasoning.
Pour soup into bowls or mugs and top each portion with toppings of choice. Serve warm. Keeps in fridge for 4-5 days and freezes well too!