Pour the oil into a deep fryer or heavy saucepan to reach halfway up the sides and heat to 325 degrees F, use a deep-fry thermometer to determine this. While the oil is heating, peel the skin off the potatoes and cut them into uniform 1/4-inch sticks; feel free to use a knife, mandoline, or French fry cutter. Dry the potato sticks thoroughly to keep the hot oil from splattering.
Fry the potatoes in batches so the pot isn't crowded and the oil temperature does not plummet. Cook the French fries for 3 minutes, until soft but not browned. Remove the fries with a long-handled metal strainer and drain on brown paper bags.
Increase the oil temperature to 375 degrees F. Return the par-fried potatoes to the oil and cook a second time for 2 minutes, or until golden and crispy. Drain on fresh brown paper bags then place in a serving bowl. Salt the fries while they're still hot and pour the parsley butter on top; toss gently to combine. Wrap the pommes frites in parchment paper cones and stick them in the bottom of mini martini shakers for serving individually.
To make the parsley butter: combine the butter, parsley, and garlic in a saucepan over medium heat. Swirl the pan around until the butter is completely melted.