In a large bowl, combine flour, granulated sugar, and salt. Add cold cubed butter and work it into the flour mixture using your fingers until you have a mix of small and medium butter pieces.
Add cold water and gently knead just until the dough comes together. Do not overwork the dough. Wrap tightly and refrigerate for at least 30 minutes.
Peel, core, and slice the apples into 5 mm thick slices. Add them to a saucepan with butter, brown sugar, cinnamon, cornstarch, salt, and water. Cook over medium heat until the apples soften and the liquid thickens to a honey-like consistency. Let cool completely.
Preheat the oven to 350°F (180°C). Reserve one-third of the dough for the lattice topping. Roll out the remaining dough on a lightly floured surface to about 3 mm thick. Transfer to a pie dish and gently press into the corners without trimming excess dough.
Sprinkle almond flour over the crust base and add the cooled apple filling.
Roll out the reserved dough to about 2 mm thick and cut into strips for the lattice. Arrange strips over the pie in a woven pattern. Trim excess dough and fold edges under to create a thick border. Crimp the edges as desired.
Whisk together the egg and 1 tablespoon water to make an egg wash. Brush over the lattice and edges, avoiding the filling. Sprinkle brown sugar on top.
Cover the pie edges with foil and bake for 30 minutes. Remove foil and continue baking for another 30 minutes, or until the crust is golden brown and the filling is bubbling.
Let the pie cool on a wire rack until slightly warm. Serve slices topped with vanilla ice cream.