In a dutch oven, or soup pot, add butter with onion, carrots, and celery.
Sauté till the vegetables soften and onions are translucent.
Add the flour and stir to evenly coat the vegetables.
Place the cauliflower into the pot. Follow with the broth and the milk.
Simmer until the cauliflower is soft. The next step is to blend the soup. I typically like a few chunks in the soup. I will set some soup to the side if using a stand blender, or I will not blend it all if using an immersion blender.
Blend soup with an immersion blender or in a stand blender. You do not need to blend the soup, but it will result in a much thinner consistency.
Add the cheese to the soup and stir to melt.
Season to taste with salt and pepper. Serve.