Heat 2 tablespoons of olive oil in a large skillet over medium heat. Add the onion and garlic, and cook until the onions begin to soften and just begin to brown, about 5 minutes.
Add the kimchi and cook for 2 or 3 minutes until it begins to crisp on the edges. Add the soy sauce and rice and stir thoroughly to combine. Cook until the rice is warmed through and beginning to brown, about 5 minutes. Transfer the rice to a bowl, and set aside.
Wipe the skillet clean with a paper towel and add 1 tablespoon of olive oil to the pan and return it to the stove set over medium heat. Crack the egg into the skillet, and immediately cover the pan with a lid. Cook until the egg white is cooked through and the yolk is barely set. Slip a spatula underneath the egg and transfer it on top of the rice. Use the yolk as a kind of sauce for the rice.