1. In a small (preferably tall) saucepan or pot, layer the potatoes and onions, seasoning with salt as you go. Add 2 cups of olive oil, plus more as needed to totally submerge the potatoes and onions. Bring to a gentle simmer over medium heat (you should see only a few tiny bubbles– it should never look like it’s sizzling or frying) and reduce heat to low. Continue to cook until the potatoes are totally cooked through (but without falling apart), 15–20 minutes (fish out a thicker slice with a fork or knife to test for doneness).
2. Meanwhile, whisk eggs and a nice pinch of salt in a medium bowl until well blended; set aside until potatoes are cooked through. Once they are, use a strainer or slotted spoon to transfer potatoes and onions to the eggs, trying to leave as much oil behind as possible. Using a spatula (and maybe your hands), mix everything until well-combined, taking care not to break the potatoes apart. Season again with salt (I keep pepper out of this, but you can add if you like).
3. To cook the tortilla, add 1½–2 tablespoons of leftover oil into a medium (8” preferred) nonstick skillet over medium-high heat. Carefully add the egg mixture, smoothing the top with a spatula, giving the skillet a few shakes so everything settles evenly. Reduce heat to medium and use your spatula to scrape up the bottom a few times to bring the uncooked egg to the bottom of the pan. Give it another shake to let everything settle once more, then let it continue to cook, shaking occasionally,, until the edges are set, the sides and underside are nicely browned (you can peek on the underside to see that the bottom is browning to your liking) and the whole thing easily pulls away from the sides of the skillet, 5 or so minutes.*
*This is not unlike making an omelet or frittata– and if you have a non-stick skillet, this will be rather effortless. If you don’t and it sticks, it won’t be the end of the world.
4. To flip the tortilla*: Grab a plate or platter larger than the skillet, and carefully place it over the skillet. Then, using a dish towel to hold the sides of the skillet firmly, flip the tortilla (with confidence!) onto the platter (it should be stunning!). Add 1 tablespoon oil to the skillet, and return it back to medium-high heat. Gently slide the tortilla off the plate back into the skillet, cooked/browned side up. For extra credit, use a spatula to gently tuck the sides underneath the tortilla to make everything nice and round. Cookanother 2–3 minutes or so, until the bottom is also set and nicely golden brown. Slide the tortilla back onto the (rinsed) platter and let it rest while you make the aioli.
*If you don’t want to flip, transfer the skillet to a 450 degree oven for 5-7 minutes, until the top is browned and everything is set. Carefully slide the tortilla from the skillet onto a cutting board or plate.
5. To make the aioli PSA: If you’re using the oil from the cooked potatoes, please make sure the oil is at least room temperature (you can pop it in the fridge to expedite the process if you need). Warm oil will not give you a good time here!
Okay, so, to make the aioli: Place egg yolk in a medium bowl. Slowly whisk in a few teaspoons of the (cooled) reserved oil. Become more confident and whisk a little bit more oil, stopping to make sure it’s fully emulsified each time. Add garlic, and then thin it out with a little sherry vinegar, white distilled vinegar, or lemon juice. Whisk in more oil until you’ve used about a cup, adjusting with water, more vinegar, and garlic as needed to keep it thick but not too thick, garlicky, and well seasoned.
6. Serve tortilla cut into thick wedges, and topped with a dollop of aioli and some or all of the friends. Dust with paprika if the spirit moves you and serve.