Soak the Korean rice cakes in warm water for about 30 minutes to soften them. Drain and set aside.
In a large skillet, heat the vegetable oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant.
Stir in the gochujang, soy sauce, and sugar, mixing well to combine.
Add the water to the skillet and bring the mixture to a simmer.
Add the soaked rice cakes to the skillet, stirring to coat them in the sauce. Cook for about 5-7 minutes, stirring occasionally, until the rice cakes are heated through and the sauce thickens.
Remove from heat and stir in the chopped green onion and sesame oil.
Sprinkle sesame seeds on top before serving.