Melt butter in a saucepan over medium heat. Whisk in flour, and cook stirring constantly for a few minutes. Remove from heat, and gradually whisk in the chicken broth so that no lumps form.
Return to medium heat, and bring to a simmer. Add watercress, cover, and cook over low heat for 20 minutes. Puree in small batches using a blender, or blend in the pan using an immersion blender. Return to the saucepan, and stir in the half-and-half cream. Heat until warm, but do not boil.