In a dutch oven or stock pot, melt the butter (or heat the olive oil) over medium heat. Add the onion and cook until translucent, about 10 minutes, stirring every now and then.

Meanwhile, chop up the cauliflower. Go here for a little lesson on cauliflower chopping.

Whisk in the flour and salt and continue stirring for about 1 minute. Slowly whisk in all the liquid: milk, water, chicken broth. Continue whisking to get rid of any clumps.

Add the chopped cauliflower and bring to a boil over high heat. This is the part where you don't want to walk away. When it boils, reduce heat to simmer and let cook for about 15 minutes, or until the cauliflower is tender.

Use an immersion blender to blend the soup. Or transfer the soup to a blender, leaving the center open to allow steam to escape. Blend in batches if necessary. Hold a towel over the top so you don't spray yourself with cauliflower lava. Pour the soup back into the pot.

Your soup will be pretty thin a this point. Never fear. Turn the heat to low and add the mustard, cayenne pepper, and 2 cups shredded cheddar cheese. Add salt and pepper to taste. The cheese should thicken it up.

Remove from heat and garnish each serving with additional cheese and green onions or chives.