Cut the potatoes lengthwise into 1/4-inch-thick slices, and then cut each slice lengthwise into 1/4-inch-thick fries.
Put the fries in a large bowl of cold water and refrigerate for at least 1 hour.
Cook the garlic and oil in a small saucepan over medium heat for 2 minutes. Strain the garlic from the oil with a small mesh strainer. Set both garlic and oil aside.
Line a baking sheet with paper towels and set aside.
Heat the oil in a large pot over medium heat, or in a tabletop deep fryer, to 325°F.
Drain the fries well and pat dry in batches with paper towels. Fry each batch, turning frequently, for 3 to 5 minutes or until the fries are a pale milky color and soft.
Remove fries with a mesh skimmer and place on the paper towel-lined baking sheet.
Increase the heat of the oil to 375°F.
Fry the potatoes again, in batches, turning frequently, until golden brown, about 3 to 4 minutes. Remove fries and drain on paper towels to remove excess oil. This will prevent the crust from absorbing oil and becoming greasy as the fries cool.
Toss fries with parsley, reserved garlic, and additional salt, to taste. Serve immediately.