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Step 1
Bring a large pot of water to a boil. While you're waiting, cut the potatoes into 1/8-inch thick slices.
Step 2
When the water boils, add 1 teaspoon salt and the potatoes and cook, stirring occasionally, until the potatoes are tender but not falling apart, 10 to 14 minutes.
Step 3
Drain the potatoes and let as much of the water drip off as possible.
Step 4
Meanwhile, put the broth and onions into an 8- or 9-inch non-stick skillet over medium-low heat.
Step 5
Cook the onions, stirring occasionally and turning down the heat if they start to brown, until they are very tender and the broth has all cooked off, 15 to 18 minutes adding more broth if needed.
Step 6
Remove onions (can put with potatoes). Wipe out the pan.
Step 7
Crack the eggs into a large bowl and beat. Season with the remaining 1/2 teaspoon salt and the pepper. Add the potatoes and onions and gently combine.
Step 8
Put the clean nonstick skillet over medium heat and coat the bottom with 1 tablespoon olive oil.
Step 9
Add the egg mixture and use a rubber spatula to press down the mixture and smooth out the top. Cook until the edges are set, then turn the heat down to medium-low. Continue cooking until the top is mostly set, 12 to 15 minutes total.
Step 10
Carefully run your spatula around and under the tortilla to make sure it's not stuck anywhere, then flip the tortilla: Turn off the heat and cover the skillet with a larger plate. Protect your hands with towels or oven mitts, then grab the pan and the plate on two sides and flip.
Step 11
Remove the pan and your tortilla will now be on the plate! Don't worry if there were a few spots that did stick, this will be the underside when you serve it anyway.
Step 12
Scrape any stuck parts off the pan and coat the bottom with the remaining 1 tablespoon olive oil.
Step 13
Slide the tortilla back in and tuck any pieces of potato that may have fallen out in the sides.
Step 14
Return the burner to medium-low, and cook until the center is no longer runny, 4 to 6 minutes.
Step 15
Transfer the tortilla to a plate and let cool for at least 20 minutes, if you can (it's best at room temperature)!
Step 16
Make the aioli while you wait: Use a microplane grater to grate the garlic into a small bowl (or use a garlic press). Add the remaining ingredients and stir to combine. Refrigerate until ready to use.
Step 17
Slice into 6 servings and serve with a dollop of the aioli.