In a large mixing bowl, whisk together the eggs, salt, and pepper. Set aside.

Peel the onion, cut it in half, and slice it into thin slices. Set aside.

Peel the potatoes, cut them in half lengthwise, and slice them into thin slices about 1/8 inch thick.

Heat oil in a 10-12 inch skillet over medium heat. Add the potatoes and cook until soft, about 5 minutes, stirring regularly to avoid browning. Remove the potatoes from the skillet into the egg mixture using a slotted spoon. 

Add the onions to the same skillet with oil. Cook them until tender and translucent, about 5 minutes, stirring regularly. Remove the onions from the skillet into the egg mixture using a slotted spoon.

Drain excess oil from the pan, leaving about 1 tablespoon. 

Chop the sardines and add them to the egg mixture. Stir it all together and pour it into the skillet over medium-low heat.

Cover the skillet and cook until the edges are completely set, about 5-7 minutes. Place a large plate over the skillet, holding it tightly. Quickly flip the omelette over onto the plate, then slide it back into the skillet to cook on the other side. Cook for an additional 3-5 minutes.

Slide the omelette out of the skillet onto a large serving plate. Garnish with sliced green onions as desired.