1. Make the crusts: Pulse flour, sugar, and 1/2 teaspoon salt in a food processor until combined. Add butter, and pulse until mixture resembles coarse crumbs with some larger pieces remaining, about 10 seconds.
2. Drizzle 1/4 cup water evenly over mixture. Pulse until mixture just begins to hold together (it should not be wet or sticky). Press dough into a disk, and wrap in plastic. Refrigerate for 30 minutes.
3. Set six 4-inch tart rings on a parchment-lined baking sheet. Roll out dough to 1/4-inch thickness on a lightly floured surface. Cut out six 5 1/2-inch circles, rerolling scraps as needed. Press dough into bottoms and up sides of tart rings, patching any holes or tears, leaving an overhang at the top of each. Trim excess dough flush with edges of rings using a knife. Refrigerate until firm, at least 1 hour or overnight. Meanwhile, preheat oven to 350°.
4. Make the filling: Peel, core, and slice each apple into 8 wedges. Toss with sugar, breadcrumbs, Calvados, lemon juice, flour, and a pinch of salt. Spread evenly on a rimmed baking sheet, and bake for 20 minutes. Stir apples, and bake until very soft and caramelized around the edges, 15 to 20 minutes more. Scrape into a bowl, and roughly mash. Let cool.
5. Assemble the tartlets: Peel, core, and quarter 1 apple. Core and quarter remaining 2 apples. Thinly slice all apples using a mandoline or a very sharp knife. Toss peeled and unpeeled apples separately with lemon juice. Spread 2 tablespoons mashed apple onto bottom of each tart shell. Fan peeled apple slices on top of mash; brush with half the butter, and sprinkle with half the sugar. Repeat with unpeeled apples and remaining butter and sugar. Bake until apples are golden brown around the edges, about 1 hour, 5 minutes. Brush tops with jam. Let cool slightly.