1) To make the crust: Whisk together the flour, salt, and baking powder. Add the butter, working it in to make a coarse/crumbly mixture. Leave most of the butter in large, pea-sized pieces.
2) Stir in the sour cream; the dough won't be cohesive. Add enough cold water to bring it together, then turn it out onto a floured work surface.
3) Pat the dough into a rough log, and roll it into an 8" x 10" rectangle. Starting with a short side, fold the dough in three like a business letter. Flip the dough over, turn it 90°, and roll it into an 8" x 10" rectangle again. Fold it in three again. Chill the dough for at least 30 minutes before using.
4) Roll the chilled dough on a lightly floured surface to a 13" circle. Place it on the round flat bottom of a tarte tatin set; or on a 12" or 14" shallow pizza pan, or other flat baking sheet large enough to hold it. Make a short crimp around the edge, no more than 1/2" high.
5) Chill the crust for at least 30 minutes. This will prevent it from shrinking as it bakes. While it's chilling, preheat the oven to 375°F.
6) Prick the chilled crust all over, and bake it for about 20 minutes, till it's golden brown. Remove it from the oven, and set it aside while you prepare the filling.
7) To make the filling: Put the butter, sugar, corn syrup, water, and pinch of salt in the bottom of a burner-safe, oven-safe 11" round pan. A cast iron skillet or our stovetop-safe ceramic pan work well.
8) Over medium heat, melt the butter and dissolve the sugar, stirring gently.
9) When the butter and sugar have completely combined (wait for the butterfat around the edge of the pan to disappear, and the mixture to turn creamy as you stir it), stop stirring and allow the mixture to bubble. Cook, stirring occasionally, till it darkens slightly, to about the shade of a palomino pony: a light, golden tan. Turn off the heat; the mixture will continue to darken as it sits.
10) Peel and slice the apples, and arrange the slices in 2 layers in concentric circles in the syrup.
11) Bake the apples and syrup for about 35 minutes, until the apples are barely fork tender. Take the pan out of the oven.
12) Place the baked crust atop the apples, crimped side down. Then take the flat, round pan on which the crust baked, and put it atop the crust. See where we're going here? We're going to flip the whole thing over, so the crust is on the bottom, the apples and syrup on top.
13) Carefully turn the apples, crust, and pans upside down. Wait a few seconds, then lift off the top pan, the ones the apples and syrup were in; the apples should have settled onto the crust. If any have remained in the pan, use a fork to transfer them to the crust. If the apples on the crust have slid to one side, very gently rearrange them so they're in their original position, covering the crust completely.
14) Serve the tarte warm, with ice cream, if desired.
Yield: 10 to 12 servings.