01 - Melt butter over medium heat in a large pot. Add chopped onion and diced carrots, sauté until softened, about 5 minutes.
02 - Incorporate minced garlic and cook for 1 minute until fragrant.
03 - Sprinkle flour evenly over vegetables; stir constantly for 2 minutes to form a roux.
04 - Gradually whisk in vegetable broth, ensuring no lumps remain.
05 - Add broccoli florets, salt, pepper, and nutmeg. Bring to a gentle boil, then reduce heat and simmer until broccoli is tender, about 12 to 15 minutes.
06 - Using an immersion blender or regular blender in batches, blend the soup until smooth or to preferred consistency.
07 - Stir in whole milk and heavy cream; heat gently over low heat without boiling.
08 - Gradually add grated cheddar cheese, stirring continuously until fully melted and smooth. Adjust seasoning as needed.
09 - Preheat oven to 375°F. Arrange bread slices on a baking sheet and bake for 6 to 8 minutes until golden and crisp.
10 - Ladle soup into bowls and garnish with extra cheddar if desired. Serve alongside toasted crusty bread.