Prepare your ingredients: If using frozen rice cakes, soak in cold water until fully thawed and separated. Cut 2 slices fish cake into bite-sized pieces. Roughly chop 2 tbsp spring onion. Peel the boiled egg and set aside whole. Measure out 1 tbsp sugar, 1 tbsp fine gochugaru, 1/2 tbsp beef dasida stock powder, 1 tbsp light soy sauce, and 1 1/2 tbsp gochujang and set alongside the stove.
Start the sauce base: Heat 2 tbsp cooking oil in a wide, deep pan over medium heat. Add 250g rice cakes and pour in 1 1/2 cups water. Add 1 tbsp sugar, 1 tbsp fine gochugaru, 1/2 tbsp beef dasida stock powder, 1 tbsp light soy sauce, and 1 1/2 tbsp gochujang. Stir well until the gochujang is fully dissolved and the sauce is a uniform deep red with no lumps remaining.
Add the fish cake: Add the fish cake pieces into the sauce and stir to coat. Place the lid on the pan and cook over medium heat, stirring every 2–3 minutes, until the rice cakes are soft and chewy all the way through with no hard centre and the sauce is thick and glossy. If the sauce thickens too quickly, add 2–3 tbsp water at a time to loosen.
Add the spring onion: Once the rice cakes are cooked through and the sauce is thick and glossy, add 2 tbsp roughly chopped spring onion and stir through well. Taste and adjust seasoning.
Add the cheese and melt: Pile mozzarella cheese generously over the entire surface of the rice cakes. Place the lid back on, turn the heat to the lowest setting, and let the cheese melt slowly until completely gooey and stretchy. Do not lift the lid during this time.
Garnish and serve: Nestle the 2 boiled egg halves yolk-side up into the cheese. Scatter dried parsley and white sesame seeds over the top. Serve immediately straight from the pan.