Rinse cut potatoes well with cold water to remove the starch (this prevents them from sticking together). Drain and dry completely to avoid splattering.

Prepare the mayonnaise: In a blender or food processor (a Vitamix is recommended), combine egg yolks, egg, lemon juice, and vinegar. Blend for 30 seconds. Add canola oil in a slow stream while blending; blend until emulsified. Add salt. Continue to blend while adding olive oil in a slow stream. Finally, slowly add in truffle oil while blending. Add roasted garlic.

Heat oil in a deep fryer to 250 degrees Fahrenheit. Add French fries and fry for five to six minutes. Remove from oil and place on a baking sheet. Place sheet in the refrigerator for half an hour, until French fries are cold.

Heat oil in a deep fryer to 350 degrees Fahrenheit. Add cooled French fries and fry again for two to three minutes, until golden and crisp. Season with salt, pepper, and parsley. Sprinkle with Parmesan cheese.

Serve truffle mayonnaise in a ramekin alongside fries.