Thinly slice the onion and cut the chicken against the grain into bite-sized pieces. Combine the water, gochujang, sugar, sake, and soy sauce in a frying pan and heat. Bring to a gentle boil then reduce heat to medium. Add the onion and chicken, then cover and simmer over medium heat. Separate the eggs into yolks and white. Thoroughly beat the egg whites. When the chicken has fully cooked through, add the egg whites, then cover and wait 30 seconds. Once the egg whites have turned white and opaque, gently beat the egg yolks and add them. Remove from heat, then cover and let the yolks cook with residual heat.
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