Step 1

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 prepared pan. Top with a second layer of potatoes, covering any gaps in first layer. Repeat layers with remaining potatoes. Drizzle any remaining duck fat in bowl over top. Cut an 8-inch square of parchment paper, and press directly onto surface of potatoes. Cover pan tightly with aluminum foil. Bake in preheated oven until potatoes are tender (removing foil to test with a wooden pick), 2 to 3 hours.

Step 2

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.

Step 3

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 7 equal strips (about 1 inch wide). Cut each strip crosswise into 3 equal pieces. Using a knife, carefully split each piece in half to form 42 (about 2 1/2- x 1-inch) pieces (about 3/4 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.)

Step 4

While potatoes are freezing, heat 1 1/2 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 1/2 teaspoons salt. Serve immediately.