Begin by preparing some kelp and dried mushroom stock. If using dashi, you can skip this step. Add mushrooms and kelp to a bowl or pot along with water and let soak for at least an hour, or preferably overnight.
Next add 1-2 tbsp of neutral oil to a dry pot over medium heat. Add potatoes and sauté for 2-3 minutes, followed by onion and sauté for another 2 minutes, or until slightly translucent. Add garlic, green onion stem and chili pepper and sauté for an additional 2 minutes.
Add your broth to the pot and bring the mixture to a boil, then lower to a simmer. Add doenjang paste, making sure it is dissolved into the soup and then your zucchini and tofu. If using mushrooms, add at this step as well.
Let simmer for 3-4 minutes, adjust to taste, adding additional chili pepper or doenjang paste as needed, then garnish with green onion tops and enjoy with rice.