Heat the oil to 375 degrees F in a heavy-bottomed pot. Preheat the oven to 200 degrees F.
Whisk together all the ingredients for the aioli.
Mix the salt, garlic powder, and paprika in a bowl and set aside.
Whisk the cornstarch and club soda in a mixing bowl. In batches, dip the potatoes in the batter, allow any excess to drip off and hold on a wire rack. Repeat with rest of the potatoes.
Fry half the potatoes, stirring occasionally until golden brown and crispy, 6 to 8 minutes. Sprinkle with the seasoning and hold in the oven on a paper towel-lined baking sheet. Repeat with the last batch of potatoes.