Soak the rice cakes: If you have cold or frozen rice cakes, soak them in warm water for 10 minutes to moisten.
Prepare the base sauce: Melt the butter in a pan on medium heat. Saute with onions until softened.
Cook the rice cakes: Put gochujang and if using,gochugaru into the pan with onions. Now slave the rice cakes, milk and fish for about 5 minutes stirring occasionally.
Add the cream: Add in the heavy cream and continue to cook over medium low until the sauce has thickened up a bit, boiling out all starchy taste of rice cakes for about 5-7 minutes.
Add cheese (optional): If using, sprinkle mozzarella cheese over the Tteokbokki, cover with a lid & let it melt.
Season and garnish: Add salt and pepper to taste. Garnish with green onions.
Serve and enjoy!: And you have a creamy rose Tteokbokki ready to be enjoyed!