01 - Melt butter in a large pot over medium heat. Add diced onion and carrot, sauté until softened, about 4 minutes.
02 - Add minced garlic and cook for 1 minute until fragrant.
03 - Sprinkle flour over vegetables, stirring constantly for 2 minutes to form a roux.
04 - Gradually whisk in vegetable broth, ensuring the mixture is smooth with no lumps.
05 - Add chopped broccoli, bring to a simmer, and cook uncovered for 10 to 12 minutes until tender.
06 - Lower heat to low. Use an immersion blender to puree soup smooth, leaving some texture if desired.
07 - Stir in whole milk and heavy cream; warm through gently, avoiding boiling.
08 - Gradually stir in grated cheddar until melted and smooth. Season with salt, pepper, and nutmeg if using.
09 - Taste and adjust seasoning as necessary. Serve hot, optional garnished with extra cheddar or fresh herbs.