Melt butter or other fat in soup pot. When the fat is bubbling, add the onions. cook until soft (ideally, cook long enough for the onions to caramelize, but you don't have to).
In a separate pot, bring part of the broth and all of the cauliflower (or potato) to a boil. When the cauliflower is soft, cool slightly and purée with am immersion blender or with a regualr blender or food processor.
To the onions, add the garlic, celery, and carrots. Stir and allow to cook until they are soft.
Add the chicken and broth and bring to a gently bubbling simmer. Stir in the puréed cauliflower (or potato) and season with salt and pepper to taste.
Turn off heat and stir in frozen peas or green beans. When they have thawed and warmed, stir in the sour cream.
Serve as is, or add toppings like more sour cream, chopped bacon, sliced green onions, cheese, etc.