01 - Melt butter in a large pot over medium heat. Add chopped onion and diced carrots, sautéing for 5 minutes until softened and fragrant.
02 - Stir in minced garlic and cook for 1 minute until aromatic, being careful not to brown.
03 - Sprinkle flour evenly over the vegetables, stirring constantly for 2 minutes to form a smooth roux and cook out the raw flour taste.
04 - Gradually whisk in vegetable broth, ensuring no lumps form. Continue whisking until the mixture is smooth and slightly thickened.
05 - Add broccoli florets, thyme, nutmeg, salt, and pepper. Simmer covered for 15 minutes until broccoli is fork-tender.
06 - Reduce heat to low. Stir in whole milk and heavy cream, heating gently without bringing to a boil to prevent separation.
07 - Using an immersion blender, purée the soup until velvety smooth, or leave some texture for a chunkier consistency.
08 - Add grated cheddar cheese, stirring constantly until completely melted and incorporated. Adjust salt and pepper to taste.
09 - Ladle hot soup into bowls and garnish with additional cheddar cheese if desired.