1. Make the tart dough by mixing the butter and sugar together in a stand mixer fitted with the paddle attachment on low-to-medium speed, until combined, about 1 minute. (But do not whip.) Add the egg yolk and mix on low speed for 30 seconds. Mix in the flour and salt on low speed, until the dough comes together. If necessary, add a sprinkle of water if the dough feels too dry. Don't overmix it.
2. Shape the dough into a disk and place in the center of a 12-inch (23cm)
removable bottom tart pan. Use the heel of your hand, and fingers, to press the
dough across the bottom and up the sides of the pan, getting it as even as
possible. Refrigerate or freeze the dough until ready to use.
3. To bake the tart, preheat the oven to 350ºF
Peel and core the apples, and cut them in eighths. Place the slices in
concentric circles in the unbaked tart shell.
4. In a bowl, whisk together the eggs and 1/2 cup sugar, along with the vanilla
extract and salt. Whisk in the heavy cream and calvados, until the mixture is
smooth.
5. Pour the filling over the apples in the tart dough. Sprinkle the top with 2
tablespoons of sugar and bake the tart until deep golden brown on top, about 45
to 50 minutes. (The tart should not leak but if you are concerned it will, bake
it on a parchment or foil-lined baking sheet.) Remove from oven and let cool on
a wire rack.
Serving: Serve the tart warm or at room temperature. Normally tarts like this
are served on their own but you can serve it with whipped cream or ice cream.