In a pan, combine water, gochujang, sugar, and soy sauce. Stir until mixed well.
Bring the sauce to a simmer over medium heat.
Add rice cakes and cook, stirring occasionally, until soft and chewy, about 10 minutes.
Add boiled eggs and cook for an additional 2-3 minutes.
Garnish with chopped green onions and sesame seeds if using.
Serve immediately and enjoy!