Soak the rice cakes in a large bowl of cold water. Use enough water to cover them. Soak for at least 30 minutes to one hour if possible. One hour is best. You are doing this to help the rice cake soften up. (Even if you buy fresh rice cake, my mom says to soak them for a while so they don’t stick together when you cook them. If soaking overnight, use cold water and place in the fridge).
Using a large wok or saucepan, heat the sesame oil over medium high heat. Add the carrots, zucchini and red bell peppers and saute for just a few minutes. Season with salt and pepper and cook for another minute or so. Add the water, brown sugar, gochujang and rice cakes. You want enough water to barely cover all of the rice cakes. Bring to a boil and then reduce to low and simmer for about 20 minutes. During the last 5 minutes, add in the mushrooms, fish cake (if using), and ramen noodles.
At this point, if you want to or need to add in cornstarch, remove a few tablespoons of liquid directly from your wok and into a small bowl. Mix with 1 tablespoon of cornstarch until completely dissolved and then pour into the wok. Mix and allow to thicken a bit. You may not need the cornstarch to thicken so you can definitely skip this if desired. Add in the green onions and cook for another 2 minutes or so. Taste your sauce! Add more sugar and/or gochujang if needed.
To serve: garnish with more green onion, sprinkle sesame seeds and serve immediately. Enjoy!