Prepare the Rice Cakes: If using dried rice cakes (tteok), soak them in warm water for at least 30 minutes or until they soften. Fresh rice cakes can be used straight away.
Prepare the Sauce: In a medium saucepan, combine the gochujang, soy sauce, sugar, minced garlic, and water (or broth). Stir well to create a smooth sauce. Bring the mixture to a simmer over medium heat, stirring occasionally.
Cook the Tteok: Add the soaked rice cakes into the saucepan with the sauce. Stir to coat the rice cakes thoroughly. Allow the mixture to simmer for about 10-15 minutes, stirring occasionally until the sauce thickens and the rice cakes become tender.
Add Fish Cakes (Optional): If using fish cakes, add them into the saucepan around the 5-minute mark, allowing them to heat through and absorb the sauce flavor.
Finishing Touches: Once the sauce has thickened and the rice cakes are fully cooked, drizzle the sesame oil over the dish for a bit of extra richness. Top with sesame seeds, chopped scallions, and a boiled egg, if desired.
Serve and Enjoy: Serve the tteokbokki hot in bowls, and enjoy the spicy, sweet, and savory flavors!