Melt the butter in a large saucepan over medium heat. Add the apples, sugar, and maple syrup and stir to combine. Cook the apples until they release some of their juices and have softened slightly, about 8 to 10 minutes, stirring every couple minutes.
Stir in the cinnamon and vanilla extract and continue cooking for another 3 minutes. Remove from heat, stir in the corn starch, and set aside to cool to room temperature.
In a large bowl, mix together the flour, hazelnut meal, sugar, and salt until combined. Cut the butter into small pieces above the bowl, stopping to stir and coat the butter bits in the flour mixture every few minutes.
Pinch the mixture together with your fingertips until it resembles the texture of damp sand. Add the water, a tablespoon at a time, mixing it with a fork, until the dough just holds together when you squeeze a fistful of it in your hand.
Preheat the oven to 400 degrees Fahrenheit.
Roll out the dough until it is 1/8-inch thick and transfer it to a 10-inch pie dish. Press the crust into the pan, trim off the excess leaving a 1-inch overhang, and reserve the excess dough. Fold the 1-inch overhang under the edge of the crust all the way around and pinch the edges.
Roll out the excess dough and use a pizza cutter to cut it into 1-inch thick long strips. Empty the cooled apple filling into the pie crust pan and arrange the strips of dough on top in a lattice pattern, pressing the edges of the lattice into the crust to seal them in place.
Whisk together the egg with 1 teaspoon of water. Lightly brush all the exposed crust with the egg wash and sprinkle with a pinch of granulated sugar.
Place the pie in the oven and bake for 20 minutes, then lower the temperature to 350 degrees Fahrenheit and bake for 40 minutes more, or until the crust is golden and the apples are soft all the way through. Remove and allow to cool for 30 minutes before slicing and serving.