Place broccoli florets into a large crock-pot. Add in diced onion, minced garlic, chicken broth, salt and pepper. Mix together and cover with the lid. Cook on low heat for 6-8 hours, or on high heat 3-4 hours.
Using either a blender or an immersion blender, blend the soup until smooth. Stir in milk and shredded cheese. Let cook for another 30 minutes.