In a 3-quart saucepan, combine potatoes, water, and salt, and bring to a gentle simmer over medium-high heat. Cook, adjusting heat as needed to maintain a gentle simmer, until potatoes are tender and offer little resistance when poked with a cake tester or paring knife, 25 to 30 minutes.

Remove from heat, strain potatoes, and return to saucepan. Set food mill fitted with plate with smallest holes over a large bowl; set aside.

Working quickly while potatoes are still hot, pass through food mill. Add cornstarch and, using a flexible spatula or wooden spoon, gently fold together until cornstarch is fully incorporated into potatoes and mixture forms a dry, crumbly 'dough.'

Divide potato-cornstarch dough evenly between two 1-gallon ziplock-style bags. Without sealing bags, roll mixture into a log to remove excess air and seal bags. Press mixture into bottom corners of bags, taking care to remove any air pockets. With the bags unsealed, use a rolling pin to spread mixture into an even 1 cm-thick layer, filling bags entirely. Seal bags and refrigerate until fully chilled, at least 1 hour and up to overnight.

Lightly dust cutting board with cornstarch. Working with one bag of chilled potato mixture at a time, cut bag open lengthwise along seams. Carefully transfer block to prepared cutting board. Cut block in half, then cut into 11.5-cm by 1-cm batons (4.5-inch by 0.4-inch). Dust cut fries with cornstarch on all sides, using a pastry brush to evenly coat newly cut sides. Transfer to a parchment-lined ½ sheet pan. Repeat with remaining bag of potato mixture.

In a large Dutch oven, heat 2 inches of oil over medium-high heat to 375 °F / 191 °C. Line a ½ sheet pan with paper towels and place it next to the stovetop. Using a spider strainer, gently lower a quarter of the cut fries into hot oil and fry for 2 minutes; fries will be very pale and will not look 'done.' Using spider, carefully transfer to prepared sheet pan. Repeat with remaining cut fries, letting oil come back up to 375 °F / 191 °C each time.

Bring oil back up to 375 °F / 191 °C. Using a spider strainer, gently lower the first batch of blanched fries back into the hot oil and fry until crispy and golden, about 2 minutes. Using spider, transfer fries to paper towel–lined sheet pan and season immediately with salt to taste. Repeat with remaining blanched fries, letting oil come back up to 375 °F / 191 °C each time.

Serve fries immediately with your favorite dipping sauces.