1. In a large pot or Dutch oven, melt the butter over medium heat. Add diced onion and cook for 4-5 minutes until soft and translucent. Stir in minced garlic and cook for another 1 minute.

2. Sprinkle the flour over the onion mixture. Stir continuously for 2 minutes to create a smooth paste and cook off the raw flour taste.

3. Slowly whisk in the vegetable broth, ensuring no lumps form. Then pour in the milk and heavy cream. Bring the mixture to a gentle simmer, stirring frequently.

4. Stir in the chopped broccoli and shredded carrots. Reduce heat to medium-low, cover, and cook for 15 minutes, until the broccoli is tender but not mushy.

5. Reduce heat to low. Gradually stir in the shredded cheddar until fully melted and smooth. Season with salt, pepper, and a pinch of nutmeg if using. Let simmer for 5 more minutes. Serve hot.