Place the egg, egg yolk, Dijon mustard, garlic, 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.

*RAW EGG WARNING

Food Network Kitchens suggest caution in consuming raw and lightly-cooked eggs due to the slight risk of Salmonella or other food-borne illness. To reduce this risk, we recommend you use only fresh, properly-refrigerated, clean, grade A or AA eggs with intact shells, and avoid contact between the yolks or whites and the shell.