Gather all the ingredients. Chop the onion, green onions, and cabbage. If you're using fish cakes, slice them as well. This prep phase keeps the cooking process smooth. It’s like laying the foundation for your dream house.

In a pot, combine the gochujang, soy sauce, minced garlic, ginger, black pepper, sugar, honey, and Korean red pepper flakes. Pour in the dashi or vegetable broth. Stir well to mix everything together. This sauce is the star of the show!

Bring the sauce to a gentle simmer over medium heat. Toss in the sliced onion and cabbage. Allow them to cook until the onion turns translucent and the cabbage softens. This can take about 5 minutes. You want just enough time for them to mingle with those spicy flavors.

Now, it’s time to add your frozen rice cakes. Stir them in, ensuring they’re well-coated with that luscious sauce. Cook for about 8-10 minutes, stirring occasionally, until the rice cakes become tender and chewy. The texture of the rice cakes is vital; they should be soft but still have a delightful bite.

If you're including fish cakes, add them now. Let everything simmer together for a few more minutes. You'll notice the sauce thickening, hugging those ingredients tightly.

Once your tteokbokki has reached the perfect consistency, sprinkle the shredded mozzarella cheese on top. Cover the pot and let it simmer for 2-3 minutes or until the cheese melts gloriously. You may want to take a moment here to appreciate the gooey goodness before serving.

Drizzle sesame oil over the finished dish, and top it with slices of green onion for that final touch. Serve hot and watch your friends and family dive in. It’s truly a sight worth seeing!