01 - Melt butter in a large pot over medium heat. Add diced onion and carrot; cook until softened, about 4 minutes.
02 - Stir in minced garlic and cook for 1 minute until fragrant.
03 - Sprinkle flour over vegetables and cook, stirring constantly, for 2 minutes to create a roux.
04 - Gradually whisk in vegetable broth, ensuring the mixture remains smooth without lumps.
05 - Add chopped broccoli; bring to a simmer and cook uncovered for 10 to 12 minutes until broccoli is tender.
06 - Reduce heat to low. Use an immersion blender to puree the soup until smooth, or retain some broccoli pieces for texture.
07 - Stir in whole milk and heavy cream; warm through gently without boiling.
08 - Gradually add grated cheddar cheese, stirring until fully melted and smooth. Season with salt, black pepper, and optional nutmeg.
09 - Taste and adjust seasoning as necessary. Serve hot, garnished as desired.