2 cups high-quality olive oil
1 sweet onion, thinly sliced
1 clove garlic, crushed slightly
3 large Yukon Gold potatoes, peeled and sliced into ¼-inch rounds
Lightly beat the eggs and season with a generous sprinkle of salt. Set aside.
In a 10-inch nonstick skillet, heat the olive oil over medium-low heat until it is warm. Add the onion and garlic and gently cook until the vegetables are translucent, about 15 minutes. Add the potatoes; cook for 20 minutes until the potatoes have completely fallen apart but the potatoes and onions haven’t taken on any color.
Remove the pan from the heat and strain the mixture through a colander, reserving the olive oil for the next time you make a tortilla. (If you continue to use this same oil, each tortilla you make will taste better than the last.) Once you’ve strained the potato-and-onion mixture, season it with salt and add the eggs, mixing until thoroughly combined.
Heat the same skillet over medium-low heat. Add one tablespoon of olive oil from the reserved potato-and-onion mixture to the pan. Pour the potato-and-egg mixture into the pan and let it cook for 2 minutes without touching the pan, until the bottom begins to set up. Gently shake the pan to release the eggs from the bottom; using a rubber spatula, gently pull the mixture away from the edge to make sure it isn’t sticking at all. Cook until the bottom is set but the top is still very wet, about 5 minutes.
Place a large, flat plate on top of the skillet, hold it tightly and, using one quick motion (probably best to perform this over the sink the first few times), flip the pan over and let the tortilla fall onto the plate.
Wipe the pan with a paper towel, return to the heat, add another tablespoon of the reserved olive oil and carefully slip the tortilla back into the pan. Using a rubber spatula, carefully tuck the edges of the tortilla back into the pan and cook for another 3 minutes. Once the bottom is set, repeat the flipping process one or two more times until the edge of the tortilla is perfectly rounded. If at any time the tortilla begins to swell, poke it gently with a fork. The tortilla should be nice and golden on the outside while remaining creamy and gooey on the inside. Remove from the pan and serve hot or at room temperature.