Stew the Potatoes: Heat the olive oil in a nonstick frying pan over medium heat, then add the sliced onion and potatoes. Turn the potatoes over, cover the pan, and gently stew for about 20 minutes, turning them 3 or 4 times with an egg flip until they are soft and cooked through. If the potatoes begin to sizzle or brown, reduce the heat. Season the Eggs: While the potatoes cook, crack the eggs into a bowl and whisk them together, then season with salt and pepper.
Drain the Potatoes: Once the potatoes are tender, use a slotted spoon to transfer them to a colander, allowing the excess olive oil to drain away.
Reserve Cooking Oil: Pour most of the remaining oil from the skillet, leaving approximately 1 1/2 to 2 tablespoons in the pan.
Preheat the Cooking Surfaces: Increase the stovetop heat to medium-high and turn the grill or broiler to high.
Add the Eggs: Return the drained potatoes to the skillet, then pour the seasoned eggs evenly over them.
Cook the Tortilla: Cook the tortilla for about 5 minutes, or until the underside is lightly golden.
Set the Center: If the center remains uncooked, place the skillet under the high grill or broiler for a couple of minutes, cooking until the center is just set.
Rest the Tortilla: Remove the tortilla from the heat and let it rest for a few minutes.
Flip onto a Platter: Place a serving platter over the frying pan, then carefully flip the pan so the tortilla turns out onto the platter upside down.
Serve: Serve the Spanish tortilla warm or at room temperature, garnished with fresh parsley.
