Pour the oil into a deep fryer (or large, heavy saucepan to reach halfway up the sides) and heat to 325 degrees F.
While the oil is heating, peel the the potatoes and cut them into uniform 1/4-inch sticks. Dry the potato sticks thoroughly on paper towles to keep the hot oil from splattering.
Fry the potatoes in batches so the sticks aren't crowded and the oil temperature does not cool. Cook the fries for approx 3 minutes, until soft but not browned. Remove the fries with a long-handled metal strainer and drain on brown paper bags.
To make the garlic butter: combine the butter, parsley, and garlic in a saucepan over medium heat. Swirl the pan around until the butter is completely melted. Lower temp and keep butter warm.
Increase the oil temperature to 375 degrees F. Return the par-fried potatoes to the oil and cook for a second time for approx 2 minutes, or until golden and crispy. Drain on fresh brown paper bags then place in a large bowl. Salt the fries while they’re still hot and pour the warm garlic butter on top; toss gently to combine. Serve hot.