01 - Melt the butter in a large pot over medium heat. Add diced onion and sliced carrots, cooking until softened, about 5 minutes. Stir in minced garlic and cook for 1 additional minute until fragrant.
02 - Sprinkle the flour over the vegetables and stir continuously for 2 minutes to cook off the raw flour taste.
03 - Gradually whisk in the vegetable broth, ensuring the mixture is smooth. Add broccoli florets and bring to a gentle simmer. Cook for 10 to 12 minutes until broccoli is tender.
04 - Lower heat to low. Stir in whole milk and heavy cream, warming the mixture until just steaming without reaching a boil.
05 - Use an immersion blender to puree the soup to your preferred consistency, either completely smooth or with some texture.
06 - Gradually add the grated cheddar cheese, stirring until fully melted and incorporated. Season with salt, pepper, and optional nutmeg.
07 - Taste and modify seasoning as necessary to suit preference.
08 - While finishing the soup, heat the crusty bread in an oven set to 350°F for 5 to 7 minutes until warm.
09 - Ladle the soup into bowls and accompany with warm crusty bread slices.