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Whisk together the eggs and milk. Heat the oil. Cook the egg until it sets.
Crack the eggs into a small bowl and add the milk. Whisk the two together until evenly blended. The egg mixture should be consistently colored throughout, with the yolks and whites well combined. Pour the oil into a clean skillet or wok. Place it on the stove over medium-high heat. As the oil heats up, turn the pan so that the oil can coat the entire bottom and all sides. Pour half of the egg mixture into the hot pan. Lower the heat to medium-low and allow the egg to cook until it no longer appears runny.  The egg mixture must evenly cover the bottom of the pan, so you may need to tilt the pan slightly immediately after pouring the eggs in. You can stir the mixture a few times immediately after pouring it into the pan, but you should stop shortly before the liquid stops spreading over the bottom surface. To help distribute the heat over the entire egg, cover the pan with a lid just before turning the heat down. If the lid is made of glass, the eggs should be done once the glass feels hot to the touch. The prepared omelette will no longer be runny, but the top surface should still look moist. Do not wait for the top to completely dry out since, by that point, the bottom will likely be burnt. Note that you will only use half of the egg mixture right now. The remaining half will be cooked in the same manner, but to minimize the number of pans you'll need to dirty, it's better to finish one omurice before cooking the rest of the eggs.