In a 3-quart sauce pan, melt butter with the chopped onion over medium-high heat. Cook until soft. Add cauliflower, potato and broth. Cover and bring to a simmer. Cook 15 minutes, or until potato is tender.
Remove from heat. Using a handheld immersion blender, puree the soup in the saucepan until smooth. Return to heat and add salt, pepper and chives. Sprinkle each serving with shredded cheddar cheese.