Prepare a large bowl with water. Julienne the potatoes, skin on, into ⅛-inch strips. To do this, use a mandoline with a julienne attachment, or slice the potatoes with a knife or standard mandoline into thin slabs and then julienne into strips. For very thin fries, you can also use a julienne peeler across the length of the potato. The slices should be the same width as a matchstick or a shoestring. For a thicker version, cut the potatoes into slices the width of a pencil.
Place the sliced potatoes into the water. Once the water becomes cloudy, rinse the fries, shaking the slices to release the starches as you rinse. Repeat, covering the potatoes with water and rinsing until the water runs clear.
Drain the potatoes and dry with a paper towel. Place on a paper-towel lined sheet tray and store in the refrigerator while preparing the oil to fry. If prepping ahead of time, store in the refrigerator for up to 6 hours. After this, the potatoes will start to shrink.
Pour the oil into a deep pot or Dutch oven and heat to 400 F. Take the fries out of the refrigerator and pat dry again, then carefully add a handful to the oil using tongs or a skimmer. Do not crowd the pot.
Fry the french fries until just beginning to brown; they will no longer be limp and will feel crispy to the touch. Remove from the oil and place on a paper-towel lined sheet tray or plate. Season immediately with a pinch of salt per batch.
Once all fries are fried and crispy, mix the melted butter and garlic together in a small bowl. Pour over the fries and toss to coat. Sprinkle on the Parmesan and parsley flakes.