Place potatoes in a bowl of cold water and agitate for 10 seconds. Transfer to fine mesh strainer and allow to drain for 5 minutes. Meanwhile, heat oil in large wok or Dutch oven over high heat to 350°F. Fry potatoes, stirring them with a wire spider until light golden brown and tender, about 4 minutes, adjusting heat as necessary to maintain oil temperature. Transfer to a paper towel-lined bowl and allow to cool for 10 minutes; reduce heat to low.

Transfer ¼ of the potatoes to the bowl of a food processor and pulse until broken down into rough ¼- to ⅛-inch pieces, about 8 1-second pulses. Transfer to a mixing bowl and repeat with the remaining potatoes, working in 3 more batches.

Add salt, starch, sugar, black pepper to taste, and any additional flavorings if desired. Gently mix with your hands to combine. Shape into cylinders about ¾-inch wide and 1-inch long.

Reheat oil to 350°F and add Tater Tots. Allow to fry for 1 minute, then gently agitate with a metal spider to separate them. Continue to cook, adjusting flame to maintain heat, until golden brown and crisp, about 4 minutes longer. Transfer to a paper towel-lined plate to drain. Season immediately with salt. Serve hot, topped as desired.