Preheat large heavy bottom pot or Dutch oven on medium heat and melt butter. Add garlic, onion, and carrots, then cook for 5 minutes, stirring occasionally.
Add butternut squash, potatoes, broccoli, vegetable broth, milk, salt and pepper. Cover, bring to a boil, then reduce heat to low and simmer for 10 minutes.
Turn off heat. Using an immersion blender, puree soup until smooth. Add cheese and stir until cheese has melted.
Serve hot sprinkled with more cheese.
Video
Notes
Store: Refrigerate in an airtight container for up to 5 days.
Freeze: Fully cook, cool completely and freeze in an airtight container for up to 3 months. Thaw on a stovetop covered on low.