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. (I often stop the mixer before the dough is done and mix it by hand, to avoid overmixing.)
2. Shape the dough into a disk and place in the center of a 9-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 (180ºC). 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.