For the crust:
5 tablespoons butter, cold
1 cup flour
1 teaspoon baking powder
1 cup sugar
1/2 teaspoon cinnamon
1 teaspoon vanilla extract
Cut the butter into small chunks. In the bowl of a stand mixer or a large mixing bowl, beat the butter, flour, baking powder, sugar, and cinnamon until the butter is the size of small peas.
Add the egg and vanilla and beat until the mixture is crumbly. Butter and flour the bottom and sides of a spring form pan or a tart pan. Using your fingers, press the crust mixture into the bottom of the pan, spreading it up the side of the pan as well. Set aside while making the filling.
For the apple pie filling:
3 Granny Smith, Braeburn, or Honeycrisp Apples
3 tablespoons sugar, divided
3 tablespoons butter
1 tablespoon pear or apple brandy
1 teaspoon cinnamon
Peel and core the apples. Slice the apples very thinly. This will look like a lot of apples, but it will all work out.
Starting from the center of the pan-filled tart pan, arrange the apples in circles, filling an entire layer of the pan. When the first layer is done, start on a second layer and a third if necessary. Repeat until all of the apples have been used.
Sprinkle the tart with 1 tablespoon of sugar and bake for 40 minutes at 350° F. Five minutes before the 40 minutes is up, melt 3 tablespoons of butter in a small saucepan. Remove the butter from the heat and mix in the egg, the remaining 2 tablespoons of sugar, the brandy, and the cinnamon with a whisk.
Remove the tart from the oven and brush with the glaze. Return the tart to the oven and bake for another 25 minutes. Cool for at least 20 minutes before slicing.