01 - Melt the butter in a large pot over medium heat. Add the onions and carrots, and sauté until softened, about 5 minutes.
02 - Stir in the garlic and cook for another 1 minute, until fragrant.
03 - Sprinkle the flour over the vegetables and cook, stirring constantly, for 2 minutes to form a roux.
04 - Slowly whisk in the vegetable broth, ensuring there are no lumps.
05 - Add the broccoli florets, salt, black pepper, and nutmeg (if using). Bring to a simmer, cover, and cook for 10-12 minutes, until the broccoli is tender.
06 - Reduce the heat to low. Using an immersion blender, puree the soup until smooth, or leave some texture if desired. Alternatively, carefully blend in batches in a blender.
07 - Stir in the milk and heavy cream. Warm gently, but do not boil.
08 - Gradually add the shredded cheddar cheese, stirring until melted and the soup is creamy and smooth.
09 - Taste and adjust seasoning as needed. Serve hot, garnished with extra cheddar and fresh herbs if desired.