Wash and cut the vegetables. For the scallions, cut into 2-inch pieces, and keep the green stems for later
In a large hotpot or donabe, heat the oil, onion, and the white pieces of the green onions over medium heat. Add the kimchi and stir together. Add the gochuhang and heat for another 30 seconds. Add the hot pepper flakes and granulated sugar, and mix all together until well-blended.
Add the 4 cups of vegetable stock, cover the lid, and let simmer. Reduce heat to medium low and add the soy sauce and miso (let the miso dissolve first on a ladle with some broth).
Add the carrots, daikon, and the tough part of the Napa cabbage and cook covered for about 10 minutes on low to medium heat. Add the leafy part of the Napa cabbage, the mushrooms, and tofu.
Add the vegetable goyza (no need to defrost frozen ones), and cook for 5 minutes over medium low heat.
Serve and top with green oinions. Add toasted sesame seeds if desired.
Note: Gyoza are also known as dumplings or pot stickers and can be found in the frozen section of most stores. Other ingredients can be found at any Asian supermarkets. A donabe is an earthenware pot that is used in Japan to make one pot meals. It can be found online. Search for donabe.