To make the dough, in a small bowl or liquid measuring cup, stir together the sour cream and ice water. In a food processor, combine the flour, sugar, baking powder and salt; pulse to combine. Scatter in the butter and pulse until the mixture resembles coarse sand with pebbly bits, 10 to 12 pulses. Drizzle in the sour cream mixture, then pulse until the mixture is curdy in appearance and clumps together, with no dry patches remaining, 20 to 30 pulses.

Lightly flour the counter and turn the dough out onto it. Lightly knead 2 or 3 times, just until cohesive. Divide in half, shape each portion into a ball, then flatten into a 4-inch disk. Lightly dust each with flour, wrap tightly in plastic wrap and refrigerate for at least 1 hour or up to 2 days.

To make the filling, while the dough chills, peel the apples. If using a box grater, one at a time, shred the apples on the large holes, rotating, until only the core remains. If using a food processor, fit it with a medium shredding disk. Cut off the sides of the peeled apples and shred them.

In a large bowl, toss the shredded apples with 40 grams (3 tablespoons) of the white sugar and the lemon juice; let stand until ready to use. Meanwhile, in a small bowl, stir together the remaining 54 grams (¼ cup) white sugar, cinnamon and salt; set aside.

When you are ready to roll out the dough, heat the oven to 375°F with a rack in the lower-middle position. Mist a 9-inch springform pan with cooking spray. If the dough pieces are too firm to roll, let stand at room temperature for 5 to 10 minutes. Dust the counter with flour, unwrap one piece and set it on the floured surface. Dust the dough with flour, then roll it into a round slightly larger than 9 inches. Transfer to a sheet of kitchen parchment, slide onto a large plate and refrigerate, uncovered, until ready to use.

Repeat with the second piece of dough, rolling it into a 9-inch round. Fit the dough into the prepared pan, pressing to level any areas that climb up the pan sides and close any gaps around the edges. Sprinkle evenly with the walnuts.

Wrap the shredded apples in a kitchen towel and squeeze to wring out as much moisture as possible. Discard any liquid in the bowl, then return the apples to it, breaking up the mass. Sprinkle with the cinnamon sugar and, using your hands, toss well, breaking up any clumps. Distribute evenly over the walnuts.

Remove the dough from the refrigerator. Peel it off the parchment and set the dough on top of the apple filling. Using a skewer, poke holes every inch or so across the surface. Place the springform pan on a rimmed baking sheet and bake until the top crust is golden brown, 40 to 45 minutes.

Let cool completely on a wire rack. Run a paring knife around the edges; remove the sides of the pan. Slide a thin metal spatula between the bottom crust and springform base, then slip the pie onto a platter. Generously dust with powdered sugar just before serving.