Heat the oil in a large pot over medium heat. Add the onions and saute for 10 minutes, until the onions are starting to brown.
Add the ginger and garlic and saute another 2-3 minutes, until they are soft and starting to brown. Stir in the curry powder and cook 1 minute, until fragrant.
Add the broth, carrots, potatoes, apple, tomato paste, worcestershire sauce, and salt, and stir to combine well. Bring to a boil, then reduce the heat to a simmer, cover, and cook for 10-15 minutes, until the potatoes and carrots are fork tender.
Place the cornstarch in a small bowl, and ladle about 2 tablespoons of the curry sauce into the bowl. Whisk to combine well, then stir into the vegetable curry.
Add the edamame and green beans. Bring the mixture up to a boil and cook 5 minutes, until the curry is thick and the green beans are tender.
Serve over rice.