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Break the eggs in a medium-sized bowl and beat the eggs lightly. To give a smooth texture, sieve through the eggs. Add the rice wine and salt then whisk them well. (If you haven’t already, move the egg mixture into a measuring cup with a handle so that it’s easier to pour it out). Add the chopped green onion.
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Heat the pan on medium-low heat and add some cooking oil. Spread it throughout the pan. Reduce the heat to low. Pour out a thin layer of egg mixture onto the pan and spread it by tilting the pan. Once the edge of the egg is cooked and the top of the egg is about 80 to 85% cooked, add a layer of cheese in the middle of the pan and start rolling the egg with a spatula and/or chopsticks.
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Push aside the rolled egg (to the left) and brush some cooking oil in the empty space (right side of the pan). Pour out another thin layer of egg mixture on the empty space and when the top of the egg is about 80 to 85 % cooked, add a layer of cheese on top of the egg and start rolling the egg with a spatula and/or chopsticks. Repeat this step until the egg mixture is used up.
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Remove the rolled egg from the pan and cool it down for 5 to 10 mins on a cutting board. Slice it into bite-size pieces. Serve. (Optionally, you can serve with some tomato sauce/ketchup or squeeze this over the egg rolls.)