Fill a large bowl halfway with water. Cut potatoes into long slices about 1/4 in. thick, then cut in 1/4-in.-thick sticks, dropping them into water as cut. Chill at least 2 hours or overnight. Drain and pat very dry.
Pour about 3 in. of oil into an 8- to 10-qt. pot; bring to 325° over medium-high heat. With a slotted spoon, carefully lower a heaping spoonful of potatoes into oil. Cook, stirring occasionally to keep fries from sticking, until potatoes are tender to the bite and ends begin to turn golden, 3 to 5 minutes. Adjust heat as needed to maintain temperature. With a slotted spoon, transfer fries to a baking pan lined with paper towels. Allow oil to return to 325° and repeat with remaining potatoes, arranging them in a single layer (you'll need a second baking pan). Let cool completely, about 15 minutes. (At this point, you can wrap fries airtight and chill up to 1 day.)
Preheat oven to 200°. Set a rack in a rimmed pan and put in oven.
In a large bowl, combine garlic, parsley, and butter. Reheat oil in pot to 375°. Remove paper towels from underneath fries. With a slotted spoon, lower 2 spoonfuls of fries into oil and cook, stirring occasionally, until crisp and deep golden, 2 to 3 minutes. With a slotted spoon, transfer fries to rack in oven and keep warm. Allow oil to return to 375°, and repeat with remaining potatoes.
Gently mix fries with parsley mixture. Season to taste with salt. Serve immediately.
Note: Nutritional analysis is per 1-cup serving.