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1
Heat the oven to 375 degrees. Peel the potatoes, then rinse them. Slice them as thinly as possible (1/16 inch thick) on a mandoline, and discard the nubby ends. Spread the potato slices on a baking sheet, sprinkle with 2 tablespoons olive oil, season with salt and toss to coat -- do this with your hands, which is the only way to coat them evenly; plus it's good for your skin.
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2
Roast the potatoes for 15 minutes. Turn the potatoes with a spatula and roast for another 10. The potatoes are done when they're tender and the ones on the perimeter are getting brown and crisp. Remove from the oven and let cool.
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3
Crack the eggs into a large bowl and whisk until blended and frothy. Add the cooled potatoes and a good bunch of pepper (I like it coarse). Blend with your hands, taking care to separate the potato slices without breaking them.
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4
Generously coat the base of a well-seasoned 9-inch cast iron (or nonstick) skillet with olive oil and set over medium heat. Crush two of the garlic cloves and add to the pan. When they begin sizzling, slide in the egg and potato mixture. Arrange and press the potatoes so they're mostly lying flat. Reduce the heat to low (or medium-low if you have a meek stove) and let cook for 20 minutes. Check from time to time, slipping a spatula under one edge and lifting, to see if the tortilla is cooking too slowly or too quickly. By the end of 20 minutes, the base should be golden brown.
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5
Now get ready to turn it -- this is the only tricky part about making tortilla. Get a baking sheet without a raised edge (or thin cutting board) and lay it, inverted, over the skillet. Then using oven mitts on both hands, lift the skillet, holding the pan on top and take it over to your sink, then swiftly invert the two, so the tortilla falls onto the baking sheet. Set down on the counter. Breathe.
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6
If any pieces stick to the skillet, pry them off and either patch up the tortilla or eat the bits. Add more oil to the skillet if needed, then slide the tortilla back into the skillet (browned side up) and place back on the heat to cook the other side, 15 minutes.
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7
Now don't hate me, but I'm going to have you flip the tortilla again and cook it for 10 more minutes on the first side. Then you can shut off the heat and call it done. Serve it at room temperature, inverted onto a platter.
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8
Time to make the aioli: combine the chives and remaining 3 cloves garlic in a food processor or blender. With the machine running, slowly drizzle in the oil through the feed tube and let it puree until the chives are fully pulverized. You may need to scrape down the sides of the bowl once or twice. Season with salt.
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9
Put the mayonnaise in a bowl. Add the chive-and-garlic oil, 1 tablespoon at a time (to taste), and blend with the mayonnaise. Adjust seasoning as desired. Serve alongside the tortilla, which should be cut into wedges.
