In a large bowl, mix together the all-purpose flour, granulated sugar, and salt. Add the cold, cubed unsalted butter and use your fingers to rub it into the dry ingredients until you reach a coarse crumb texture. Gradually add cold water, a tablespoon at a time, until the dough forms. Shape the dough into a disk, wrap it in plastic, and refrigerate for 30 minutes.

While the dough chills, peel, core, and slice the three medium apples. In a large skillet over medium heat, melt 75 g of unsalted butter. Once melted, add the sliced apples, brown sugar, cinnamon, salt, and water. Cook for about 10-12 minutes until the apples are tender but not mushy. Remove from heat and let the filling cool slightly.

Preheat your oven to 190°C (375°F). Take half of the chilled dough and place it on a floured surface. Roll it out to fit your pie dish, ensuring it's about ⅛-inch thick. Gently transfer the rolled dough into the dish and trim any excess. Sprinkle 5 tablespoons of almond flour evenly over the bottom to absorb moisture from the filling.

Carefully pour the cooled apple filling into the prepared pie crust. Roll out the remaining dough, and you can either cut it into strips for a lattice top or use it as a full crust. If opting for a lattice, weave the strips over the apples, then crimp the edges to seal tightly and prevent leaks during baking.

In a small bowl, whisk together 1 egg and 1 tablespoon of water to create an egg wash. Brush this mixture generously over the top of the pie crust for a golden finish. Optionally, sprinkle brown sugar over the crust for added sweetness and a nice crunch.

Carefully place the assembled pie in the preheated oven. Bake for approximately 50-60 minutes, or until the crust is golden brown and the filling is bubbly. Keep an eye on the pie, and if the edges brown too quickly, shield them with strips of aluminum foil.

Once baked, remove the pie from the oven and let it cool on a wire rack for at least 30 minutes. This cooling step allows the filling to set beautifully. The Apple Pie à la Mode is best served warm, where the crust maintains its flakiness.

Slice the warm pie into generous portions and serve each slice topped with a scoop of creamy vanilla ice cream. The contrast of warm apple filling and cold ice cream is a comforting way to enjoy this delightful dessert.