Once the broccoli is tender, use an immersion blender to puree some of the soup, until it is mostly smooth, but still with some chunks. Whisk together the milk, cream and flour and stir it into the soup, along with the cheeses. Place the lid back on and set the heat to high. Let this cook another 30-45 minutes, or until the soup has thickened slightly, is fully heated through and the cheese has fully melted. Taste and add more seasonings if it needs it, then serve.