In the bowl of a food processor, pulse the flour, salt, and butter until it resembles coarse meal. With the machine running, pour in the yolks and 3½ tablespoons cold water and mix just until the dough holds together. Turn the dough onto a flat surface and flatten into a disc. Wrap in plastic wrap and refrigerate for 1 hour, or until firm.
Preheat the oven to 350°F. Lightly flour a work surface and roll the dough into a round large enough to fit a 10- to 12-inch tart or quiche pan with 1½- to 2-inch-tall sides. Fit the dough in the bottom and up the sides of the pan. Trim excess dough even with the pan’s rim. Line with parchment paper and fill with rice or beans to weigh down the dough. Bake for 15 minutes, remove the tart shell, and reduce the oven temperature to 325°F. Remove the weights and paper from the dough and return to the oven to bake for another 15 minutes, or until light golden brown.
For the Filling
In a large bowl, toss the apples with ¼ cup of the powdered sugar and set aside at room temperature for 30 minutes. In a large sauté pan over high heat, lightly brown the butter, add the apples, and toss to coat. Add the honey and cook, stirring, until the apples are golden brown and about halfway cooked. Remove the pan from the heat, pour in the calvados, and carefully flambé. Simmer, stirring, until glazed. Set aside.
In a medium bowl, whisk the cornstarch and sugar to combine. Add the eggs, yolk, crème fraîche, and vanilla paste and whisk until smooth. Stream in the milk, while whisking, to make a smooth batter.
Fan the apples into the tart shell in a single layer. Pour the batter over the top to the rim (reserve any extra). Bake for 30 to 35 minutes, until a cake tester inserted into the center comes out clean. If the filling sinks while baking, pour in the reserved batter about halfway through.
Remove from the oven and dust with the remaining ½ cup powdered sugar.