Put the cheonggukjang (fermented soybean paste) and water in a pot and bring to a boil.
Cut tofu, zucchini, onion, and shiitake mushrooms into bite-sized pieces.
Add the prepared vegetables and tofu to the boiling cheonggukjang.
Mince garlic and chili peppers, add them to the pot, and let it boil.
Season with soup soy sauce and salt to taste.
Boil for 10 minutes, then serve.