Wash, cut, and trim the broccoli florets and keep the stem and cut offs for the soup. Keep the firm and green florets for another recipe.
Use a vegetable peeler or a paring knife to remove the outer layer of the broccoli stems to reveal the tender part. Coarsely chop the heart of the stems.
Melt the butter over a low heat and sweat the broccoli stems and trimmings with a pinch of salt.
Add chicken or vegetable stock up to the level of the broccoli, cover with a lid and let it cook until tender.
Blend the broccoli soup with the cream cheese and adjust the texture with some extra stock if necessary. Season to taste and serve.