In a large skillet over medium-high heat combine potatoes, green beans, thyme, pepper, Worcestershire sauce and 3/4 cup of broth. Bring to a boil; reduce heat to medium-low, cover and simmer 15 to 20 minutes or until vegetables are tender.
In a small bowl blend remaining broth and cornstarch. Stir in parsley; add to potato mixture. Cook, stirring, until bubbly and thickened.