Add carrots, broccoli, salt, pepper, and broth. Bring to a simmer, cover pot and simmer for 15 minutes.
At this point if you would like to blend - remove from heat and use an immersion blender. Or, in batches, use a regular blender, then return to pot. I blend about half of soup.
Add milk, and cream. Heat through. Remove from heat. Add cheese and stir.