01 - Melt butter in a large pot over medium heat. Add chopped onion, minced garlic, diced carrot, and celery. Cook for 5 minutes until softened and fragrant.
02 - Sprinkle flour over the sautéed vegetables and stir continuously for 1 minute to cook out the raw taste.
03 - Slowly pour in vegetable broth, stirring constantly to prevent lumps from forming.
04 - Add broccoli florets and bring to a boil. Reduce heat to low, cover, and simmer for 10–12 minutes until broccoli is tender.
05 - Use an immersion blender to blend the soup until smooth, or transfer in batches to a countertop blender, then return to pot.
06 - Stir in whole milk, heavy cream, sharp cheddar, and Parmesan cheese. Heat gently, stirring frequently until cheese melts and soup achieves a creamy texture.
07 - Season with salt, freshly ground black pepper, and nutmeg to taste. Serve hot, optionally garnished with additional cheese or croutons.