Add the diced onion and cook until translucent, about 5 minutes.
Stir in the minced garlic and sauté for an additional 1 minute until fragrant.
Add the broccoli florets and vegetable broth to the pot. Bring to a boil, then reduce heat and let it simmer for 15-20 minutes, until the broccoli is tender.
Using an immersion blender, carefully blend the soup until smooth. (You can also transfer it to a blender in batches if you don’t have an immersion blender.)
In a small bowl, mix the flour with a tablespoon of water to create a smooth paste, then add it to the soup to thicken.
Stir in the heavy cream, Dijon mustard, and nutmeg, and cook for another 5 minutes over low heat.
Gradually add the grated cheddar cheese, stirring until completely melted and the soup is creamy.
Season with salt and pepper to taste, adjusting the flavors as needed.