Gather the ingredients. Preheat oven to 300°F.

Line an 8-inch square baking pan with parchment paper, allowing 2 inches of overhang on all sides. Toss together potatoes, duck fat, and 1 tablespoon salt in a large bowl until well coated.

Place a single layer of potatoes in a prepared pan. Top with a second layer of potatoes, covering any gaps in the first layer. Repeat layers with remaining potatoes. Drizzle any remaining duck fat in a bowl over the top.

Cut an 8-inch square of parchment paper and press it directly onto the surface of the potatoes. Cover the pan tightly with aluminum foil. Bake in a preheated oven until potatoes are tender (removing foil to test with a wooden pick), 2 to 3 hours.

Transfer pan to a wire rack and remove foil, leaving parchment sheet on potatoes. Set a second 8-inch square pan on top of potatoes in pan and weigh it down with unopened canned goods. Let cool to room temperature, about 1 hour. Chill potatoes 8 hours or overnight with weighted pan on top.

Remove weighted pan and top parchment sheet; discard parchment sheet. Run a knife around edges of pan to loosen potato cake. Invert potato cake onto a cutting board; remove and discard parchment liner.

Cut potato cake into seven equal strips (about 1-inch wide). Cut each strip crosswise into three equal pieces.

Using a knife, carefully split each piece in half to form 42 (about 2 ½- x 1-inch) pieces (about ¾-inch thick).

Transfer potato pieces to a baking sheet lined with parchment paper and freeze until solid, at least 30 minutes or up to 1 month. (If freezing to use at a later date, transfer frozen potato pieces to a large ziplock plastic freezer bag.)

While potatoes are freezing, heat 1 ½ inches of oil in a Dutch oven over medium-high to 375°F. Working in batches, fry frozen potato pieces (keeping remaining pieces frozen), turning occasionally, until golden brown and crispy, 5 to 6 minutes.

Using a slotted spoon or spider, transfer potato pieces to a brown paper–lined rimmed baking sheet. Sprinkle fried potatoes evenly with remaining 1 ½ teaspoons salt. Serve immediately.