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