Prepare the vegetables: Chop the broccoli into small florets. Dice the onion and mince the garlic.

Sauté the aromatics: In a large pot, melt the butter over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes. Add the minced garlic and cook for another minute.

Make the roux: Sprinkle the flour over the onions and garlic. Stir continuously for about 2 minutes to cook the flour and form a roux.

Add the broth: Gradually pour in the chicken or vegetable broth while stirring to avoid lumps. Bring the mixture to a simmer.

Cook the broccoli: Add the broccoli florets to the pot. Simmer for about 10-12 minutes, or until the broccoli is tender.

Blend the soup: Use an immersion blender to partially blend the soup, leaving some chunks of broccoli for texture. Alternatively, transfer half of the soup to a blender, blend until smooth, and return it to the pot.

Add the cheese and cream: Reduce the heat to low. Stir in the shredded cheddar cheese until fully melted. Then, add the heavy cream, salt, black pepper, and nutmeg (if using). Stir well to combine.

Serve: Ladle the soup into bowls and garnish with extra shredded cheddar cheese or a sprinkle of black pepper if desired.