Making this soup is as rewarding as it is straightforward. Just follow these steps:

1. In a large pot, melt the butter over medium heat. Add the chopped onion and garlic, sautéing until they become translucent and fragrant, about 3-4 minutes. This step always reminds me of my mom, who taught me that a good base is the soul of any dish.
2. Sprinkle in the flour, stirring constantly for about a minute to form a roux. This will help thicken your soup.
3. Gradually whisk in the vegetable broth, ensuring there are no lumps. Bring the mixture to a gentle simmer.
4. Add the broccoli florets, cover, and let them cook until tender, about 10 minutes. This is when the kitchen starts to fill with that comforting aroma that makes my heart feel right at home.
5. Reduce the heat to low, and slowly pour in the milk, stirring to combine.
6. Using an immersion blender, blend the soup to your desired consistency. I like mine with a bit of texture, but you can make it as smooth as you like.
7. Stir in the grated cheddar cheese, allowing it to melt completely into the soup. Add a pinch of nutmeg, salt, and pepper to taste. The nutmeg is my secret touch, adding warmth and depth to the flavor.
8. Serve hot, garnished with extra cheese or croutons if you like.