Add the oil to a large pot over medium-high heat. Cook the onions and garlic for 8 minutes, then add the ginger, and cook 2 more minutes.
Add the vegetable broth, carrots, potatoes, mushrooms, apple, tomato paste, Worcestershire sauce, curry powder, garam masala, salt, and pepper. Bring to a boil, then lower to a simmer, and cook for 15 minutes, or until the potatoes are tender.
To make the cornstarch slurry, whisk together ½ cup of the curry broth, and the cornstarch, until there are no clumps. Add this mixture back into the pot, and stir.
Add the frozen edamame, and cook on low for 10 more minutes. The Japanese curry is ready, and can be served optionally with parsley, scallions, and rice.