Mix the eggs in the a bowl with salt, a few turns of black pepper, and the mirin.
Heat the oil in a nonstick skillet. Sauté the zucchini, (or other vegetables) scallions, and kimchi for 2 minutes, stirring occasionally.
Add the eggs and cover the skillet, and let cook for 2 minutes over moderate heat.
Remove the lid and fold the omelet in half and cook further if you prefer your omelets more cooked.
Serve with additional kimchi on the side if you like.