Place the egg, egg yolk, Dijon mustard, garlic puree, salt, and pepper in a food processor fitted with a metal blade and process until well blended.
With the processor running, slowly pour in the oils, gradually increasing the amount added as the sauce thickens. As soon as the sauce is very thick, thin with lemon juice, followed by the remaining oil. Place in a medium bowl and check for seasoning, adding more lemon juice, salt and pepper if necessary.
Peel potatoes and slice into 1/4-inch slices. Cut each slice in 1/4-inch strips, and rinse in cold water.
Heat the oil to 315 to 325 degrees F.
In 4 to 5 small batches, blanch the fries for approximately 8 minutes, or until golden brown. Drain on paper towels.
When ready to serve, heat oil to 350 to 375 degrees F.
In small batches, fry blanched potatoes for 2 to 3 minutes, until golden brown and crispy. Drain well, and toss in mixing bowl with chopped parsley and salt and pepper. Serve with Dijon aioli.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.
Recipe courtesy of Charlie Palmer, Aureole Restaurant