Heat 2 tablespoons of oil in a nonstick skillet and fry the onion over medium-low heat until translucent, about 8 minutes. Remove from the pan and set aside.
In a separate bowl, beat the eggs with a hand mixer. Break the potatoes into small pieces and add them to the eggs. Add the onion, milk and stir them making sure they are well integrated.
Heat the rest of the oil over medium-high heat in the same skillet where you fried the onion. Pour the mixture and lower the temperature to medium heat, cover it and let it set on that side. Flip it over with the help of a lid or plate. Cook for about 2 to 3 minutes on each side.