01 - Melt butter in a large pot over medium heat. Add chopped onion and diced carrots, sautéing for 5 minutes until vegetables are softened and fragrant.
02 - Stir in minced garlic and cook for 1 minute until aromatic. Sprinkle flour evenly over the mixture, stirring constantly for 2 minutes to create a smooth roux without browning.
03 - Gradually whisk in vegetable broth, ensuring no lumps form. Add broccoli florets, thyme, nutmeg, salt, and pepper. Bring to a gentle simmer and cook for 15 minutes until broccoli is fork-tender.
04 - Reduce heat to low. Pour in milk and heavy cream, stirring gently to combine. Using an immersion blender, puree the soup until smooth while leaving some texture for body. Alternatively, blend in batches using a countertop blender.
05 - Add grated sharp cheddar cheese, stirring continuously until completely melted and incorporated. Taste and adjust seasoning as needed. Serve immediately in warmed bowls, garnished with additional cheddar if desired.