For the Crust:

1. Set out a clean 9-inch-round tart pan.
2. In a small bowl, whisk together the egg yolk, water, and vanilla. Set aside.
3. In a large bowl, whisk together the flour, sugar, and salt.
4. Cut the butter into the flour mixture until all of the butter pieces are no larger than small peas throughout.
5. Add the egg mixture, and mix with your hands until everything is combined and comes together to form a dough.
6. Transfer the dough to a lightly floured work surface. Use a floured rolling pin to roll out the dough in a circle shape until it is a little larger than the size of the 9-inch tart pan.
7. Transfer the dough to the tart pan. Use your fingers and hands to press the dough into the bottom and up the sides of the pan. Cut off any excess dough.
8. Let chill in the refrigerator while you prepare the filling.

For the Filling:

1. Preheat oven to 425°F.
2. Peel, core, and thinly slice the apples for the filling. If they are small, use 5.
3. In a large saucepan, combine all of the filling ingredients. Cook the mixture over low heat for about 15 minutes, stirring occasionally, until the apples are soft enough that a fork can easily be inserted into a slice.
4. Remove from the heat and let cool completely in the pan while you slice the remaining apples.

To Assemble and Bake:

1. Core and thinly slice the remaining 2-3 apples for the topping. If they are small, use 3.
2. Spread the cooled apple mixture into the bottom of the chilled tart crust. Arrange the sliced apples decoratively on top.
3. Evenly dot the top of the tart with the pieces of butter.
4. Place in the oven and bake for 10 minutes. Lower the temperature to 350°F and bake for an additional 50-60 minutes, or until the apples are soft and browned on top and the crust is golden.
5. Remove from the oven. While still warm, brush with maple syrup all over the top of the fruit to create a thin glaze.
6. Serve warm or cold. Store in the refrigerator.