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1
Preheat oven to 425 F and line a large baking sheet (or two small ones) with parchment paper.
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2
Scrub sweet potatoes clean, and with the skin left on, cut the potatoes into roughly 1/2 inch wide and 4 inch long pieces.
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3
In a large bowl, toss the pieces of sweet potato with the paprika, onion powder, salt and pepper, and enough olive oil to lightly coat each piece.
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4
Arrange seasoned potatoes on the baking sheet(s), leaving a little space between each piece to allow room for them to breathe (at least half an inch - otherwise the potatoes will get soggy). Bake until golden brown, about 25 minutes, turning pieces halfway during the baking.
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5
Prepare the aioli while the potatoes are baking:
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6
Start by warming a medium mixing bowl under hot water. This step will help warm up the egg yolk quickly. Dry the bowl completely, then add in the egg yolk and whisk rapidly until it is thick and sticky, 1 to 2 minutes.
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7
Add the lemon juice, garlic and salt, and whisk again for 30 more seconds.
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8
Now start slowly adding the oil to the yolk, drip by drip, whisking all the while. It is important to whisk continuously at the beginning. Stop pouring and continue to beat the mixture every ten seconds to assure that the yolk is properly absorbing the oil.
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9
Keep doing the previous step until the mixture thickens into the texture of heavy cream. If you've reached this point, you can relax a little, and start drizzling the rest of the oil a little faster than dorp by drop, but still at a slow drizzle. Soon the mixture will thicken and stiffen more until it resembles mayonaise. If it becomes to thick, you can always add a little more lemon juice to thin it out a bit.
