Wash broccoli, cut into florets, dice onion, and mince garlic.
Melt butter in a large pot over medium heat, sauté onion for 5 minutes, then add garlic and cook for 1 minute.
Add vegetable broth and broccoli, bring to a boil, then simmer for 10-15 minutes until broccoli is tender.
Blend the soup until smooth using an immersion blender or countertop blender.
Return to low heat, stir in milk and cheese until melted, season with salt, pepper, and optional red pepper flakes.
If desired, mix cornstarch with water and add to the pot, cooking for an additional 2-3 minutes.