To make a broccoli and cheese soup with cream, combine 2 quarts chicken broth, 4 chopped broccoli heads, 1 chopped onion, 2 chopped carrots and 1 bay leaf in a pan over medium heat. Bring mixture to a boil, stir in cheese until melted, and add half and half cream.
Remove the bay leaf before eating the dish. Replace half and half cream with heavy whipping cream for a creamier soup.
Alternatively, melt 1/2 cup of unsalted butter in a large pot over medium heat. Add 1 finely chopped yellow onion and cook until soft. Sprinkle 1/3 cup of flour over onions and stir to combine, then slowly mix in 4 cups of whole milk and 2 cups of half and half. Add a pinch of nutmeg, 4 heads of chopped broccoli a dash of salt and lots of freshly ground black pepper. Cover and reduce head to low, simmer for 20 to 30 minutes or until the broccoli is tender, and then add 12 ounces of mild cheddar cheese a handful at a time, and stir until melted. Use an immersion blender or potato masher to break up the broccoli, whisk in 2 cups of vegetable broth, reheat if necessary and serve.