For the kimchi vegetables
Stir together the garlic, ginger, fish sauce, gochujang paste, sugar, rice wine vinegar, and warm water in a large bowl until the sugar has dissolved.
Add the sesame seeds, cabbage, cucumber, and beansprouts, mixing thoroughly with your hands to coat in the sauce.
Cover the bowl and leave overnight to ferment. The next day, chill until ready to use.
For the steak
Whisk together the soy sauce, vinegar, and sugar in a mixing bowl.
Stir in the steak slices, coating them in the marinade.
Heat the oil in a large wok set over a high heat.
Add the steak and stir-fry until browned all over, about 3-4 minutes.
Remove from the wok and cover loosely with aluminium foil to keep warm.
For the seasoned greens and carrots
Bring a large saucepan of salted water to the boil.
Blanch the carrots and spinach in the water for 30 seconds.
Drain well and let cool briefly before squeezing out the excess water from the spinach leaves.
Whisk together the sesame oil, garlic, and sesame seeds in a mixing bowl.
Add the spinach and carrots, stirring to combine.
Heat the oil in a large non-stick frying pan set over a moderate heat.
Crack the eggs into the pan and leave to cook until the whites are set, about 2 minutes.
Partially cover the pan with a lid and cook for a further 1-2 minuets until the yolks are just set.
Remove the pan from the heat.
Arrange the kimchi vegetables, steak, seasoned greens and carrots in serving bowls with fresh beansprouts and fresh cucumber slices.
Sit the fried eggs on top and serve with a sprinkling of black and white sesame seeds.