In a small bowl, combine the sauce ingredients. Mix well.
Bring a medium pot of water to a boil over high heat. Add the sheets of eomuk and cook for 30 seconds. Drain and cool. Once they are cool, cut the eomuk into ½-inch strips.
In a large pan over medium-high heat, warm ½ tablespoon vegetable oil. Add onion and carrot. Saute until slightly softened, about 3 minutes. Add the fish cake and stir for another 2 minutes. Add the sauce, mix well and cook for another 2 minutes. Serve warm or at room temperature.