In a large pot over medium heat, melt the butter. Add the chopped onions and minced garlic, and sauté until the onions become translucent (about 5 minutes).
Add the broccoli florets to the pot and cook for another 5 minutes, stirring occasionally.
Sprinkle the flour over the broccoli mixture, stirring continuously to combine, and cook for about 2 minutes.
Gradually pour in the vegetable broth while continuously stirring to avoid lumps. Bring the mixture to a boil.
Once boiling, lower the heat and let it simmer for about 10 minutes, or until the broccoli is tender.
Using an immersion blender, carefully blend the soup to your desired creaminess. If you prefer a chunkier texture, blend only half the mixture.
Stir in the milk, cheddar cheese, salt, pepper, and nutmeg. Cook on low heat until the cheese is melted and the soup is heated through, about 5 more minutes.
Adjust seasoning as needed and serve hot.
Notes
Ladle the soup into deep bowls, and sprinkle with croutons and extra cheese on top for a delightful finish.