We got this recipe from the amazing Pioneer Woman and it is so good that I had to type it out so I'll never lose it (I'm making my daughters a cookbook from this blog.)
Sprinkle flour evenly over the top and stir to combine. Pour in broth and stir well. Allow this to thicken for 3 or 4 minutes, then reduce heat to low. Stir in half-and-half, then cover and allow to simmer/thicken for 15 minutes or so.
Stir in cheeses and green onions. When cheese is melted and the soup is hot, check seasonings. Add salt and pepper as needed.
Ladle into hollowed out boules and serve immediately