In a medium pot over medium-high heat combine vegetable broth, thyme, parsley and potatoes. Bring to a boil and reduce heat to low. Cook, covered, for about 10 to 20 minutes, or until potatoes are tender; drain, reserving broth.
In a small bowl combine cornstarch and water; add to broth and cook, stirring constantly, over medium heat until mixture thickens into a sauce.