For great broccoli cheese soup, gather 1 head broccoli, 1 onion, 1 carrot, 1/4 cup flour and 2 1/2 cups grated cheddar. Also organize 2 cups half-and-half, 3 cups chicken broth, 2 bay leaves and 1/4 teaspoon nutmeg. Simmer for 20 minutes, puree the vegetables, then add cheese to finish.
Over medium heat, melt 6 tablespoons of butter in a Dutch oven. Add the chopped onion and allow it to brown and soften, then add the flour, letting it turn golden as well. Next, add the half-and-half, whisking everything together until the contents are smooth. Introduce the broth, nutmeg, bay leaves, some salt and pepper, and simmer over medium-low for about 20 minutes, or until thickened.
Add the chopped carrots and broccoli florets to the stock, simmering until everything is tender. Remove the bay leaves, then puree the soup in batches inside a food processor, returning each to the Dutch oven afterwards. Next, add the cheese to the soup, and continue simmering and stirring until it is fully melted and incorporated. If the broth becomes to thick at this point, add approximately 3/4 cups of water. For a classic service option, remove the insides of several small sourdough bread boules with a sharp knife so that only a thick crust remains.
Ladle the finished soup inside each of the bread boules. Garnish with extra shredded cheese.