01 - Melt butter in a large pot over medium heat. Add onion and garlic, sauté until softened and fragrant, approximately 3 minutes.
02 - Stir in carrots and cook for 2 minutes. Add broccoli florets and sauté for an additional 2 minutes.
03 - Sprinkle flour over vegetables, stirring well to coat. Cook for 1-2 minutes to eliminate raw flour taste.
04 - Gradually whisk in vegetable broth, ensuring no lumps form. Bring to a simmer and cook for 10-12 minutes until carrots and broccoli are tender.
05 - Reduce heat to low. Add milk and cream, stirring gently. Simmer for 5 minutes—do not boil.
06 - Use immersion blender to partially puree for creamy texture, leaving some vegetable pieces for bite. Alternatively, blend half the soup in a regular blender and return to pot.
07 - Stir in cheddar cheese, salt, pepper, and nutmeg if using. Mix until cheese is melted and soup is smooth.
08 - Taste and adjust seasoning if needed. Serve hot, garnished with extra cheddar and fresh herbs if desired.