How to Make It
In a small bowl, whisk the vinegar, egg yolk, garlic and cayenne. Slowly whisk in the 2/3 cup of olive oil until incorporated. Season with salt.
Spread the flour in a shallow bowl. In a second shallow bowl, whisk the whole egg with 1/3 cup of the aioli. In a third shallow bowl, spread the panko. Season the chicken with salt and pepper, then dredge in the flour and shake off the excess. Dip the chicken in the egg mixture, then dredge in the panko, pressing to help it adhere.
Set a wire rack over a rimmed baking sheet. In a large, deep skillet, heat 1/4 inch of olive oil until shimmering. In batches, fry the chicken over moderately high heat, turning once, until golden brown, about 3 minutes. Transfer to the rack and season with salt. Serve with the aioli and fries.