Heat oil in an 8-inch or 10-inch skillet, over medium-high heat. Add in mushrooms, and cook until they just begin to soften.
Then add in garlic and ginger, and continue to cook until mushrooms are softened. Add in yellow onion and zucchini and cook for about 2-3 more minutes.
Add in the vegetable stock or water, along with soy sauce, sugar, and gochujang. Stir well to mix in the seasoning. Raise heat to high and bring soup to a boil.
Lower heat to bring soup to a slow boil, and gently add in the tofu, carefully spreading the pieces across the skillet. Add in kimchi and the Spicy Korean Chili Seasoning.
Then reduce heat to medium-low, and let simmer for about 5-7 minutes (you want to keep the stew simmering hot the whole time, adjusting the heat as necessary).
Finally, swirl in toasted sesame oil, give it a quick stir, and turn heat off.
Serve the Korean Tofu Stew steaming hot in the skillet. Garnish with scallions. Enjoy it with a bowl of white rice and glass of cold beer.