01 - Melt butter in a large pot over medium heat. Add chopped onion and diced carrots, cooking until softened, about 5 minutes.
02 - Stir in minced garlic and cook for 1 minute until fragrant.
03 - Sprinkle flour over the vegetables and stir continuously for 2 minutes to form a roux.
04 - Gradually whisk in the vegetable broth, ensuring the mixture remains smooth without lumps.
05 - Add broccoli florets, salt, pepper, and optional nutmeg. Bring soup to a simmer, cover, and cook for 15 minutes until broccoli is tender.
06 - Use an immersion blender to puree the soup until desired consistency is achieved, or carefully transfer in batches to a blender.
07 - Reduce heat to low. Stir in whole milk and heavy cream, followed by shredded cheddar cheese, mixing until fully melted and smooth.
08 - Taste the soup and adjust seasoning if necessary. Serve hot, optionally garnished with extra cheese or fresh herbs.