Peel and slice the potatoes into match-stick sized fries. Keep the potatoes in a large bowl of water while you continue to cut the remaining fries to prevent them from browning.

After peeling and slicing potatoes, place the potatoes and vinegar in a large stock pot and add 2 quarts of water and 2 tablespoons of kosher salt. Bring to a boil over high heat. Boil for 8 minutes until the potatoes are tender, but not falling apart.

Drain and spread the potatoes on paper towel-lined baking sheet and allow to dry for at least 10 minutes.

Meanwhile, heat the oil in large Dutch oven to 400°F.

Add a handful of the fries to oil, making sure the oil temperature does not drop lower than 350 degrees. Cook for 60-90 seconds, stirring occasionally with wire mesh spider strainer. After 60-90 seconds, remove them to another paper-towel lined baking sheet.

Repeat with remaining potatoes, allowing oil to return to 400°F after each addition.

Once you've fried the potatoes the first time, allow them to cool to room temperature for about 30 minutes.

Return oil to 375°F/ high heat. Fry the potatoes a second time in batches until crisp and light golden brown, about 2-3 minutes for each batch, adjusting the heat as needed to keep a consistent temperature. Once crisp. remove the fries with a wire mesh strainer and transfer to a bowl lined with paper towels and season immediately with kosher salt and pecorino cheese. Serve immediately with basil scattered on top.