Heat the butter in a large pot or dutch oven over medium heat until melted. Add the onions and sauté until translucent, about 4 minutes. Add the cauliflower florets and the chicken broth. Bring the mixture to a boil and simmer, uncovered, at least 20-25 minutes, or until the cauliflower is quite tender (if the cauliflower still has a bite to it, your soup will be grainy).

Working in smaller batches, transfer the mixture to a blender*, hold down the top of the blender with a kitchen towel, and whirl until smooth and creamy. Return the soup to the pot over medium heat and stir in the cheddar cheese. If your soup is too thick at this stage, add more chicken broth or water to reach desired consistency. Season with salt and pepper to taste.

Serve while quite hot with a pinch of cayenne pepper or smoked paprika, fresh chives, and grated cheddar.