Mix Dry Ingredients: In a large mixing bowl, combine the all-purpose flour and salt.

Incorporate Butter: Add the chilled, cubed butter to the flour mixture. Use a pastry cutter or food processor to blend until the mixture resembles coarse crumbs.

Add Ice Water: Gradually add ice water, one tablespoon at a time, mixing until the dough begins to come together. Avoid adding too much water; the dough should be just moist enough to hold together.

Form Dough: Divide the dough into two equal portions, shape each into a disk, wrap in plastic wrap, and refrigerate for at least 1 hour.

Combine Fruits: In a large bowl, mix the sliced apples and strawberries.

Add Flavorings: To the fruit mixture, add granulated sugar, cornstarch, lemon juice, ground cinnamon, ground nutmeg, and vanilla extract. Stir well to ensure the fruit is evenly coated.

Preheat Oven: Set your oven to 375°F (190°C).

Roll Out Bottom Crust: On a floured surface, roll out one disk of dough into a circle approximately 12 inches in diameter. Carefully transfer it to the 9-inch pie dish, pressing it gently into the bottom and sides.

Add Filling: Pour the prepared fruit filling into the crust-lined pie dish. Dot the filling with small pieces of unsalted butter.

Roll Out Top Crust: Roll out the second disk of dough. You can place it whole over the filling or cut it into strips to create a lattice pattern.

Seal Edges: Trim any excess dough and crimp the edges to seal. If using a whole top crust, cut a few slits to allow steam to escape.

Apply Egg Wash: In a small bowl, whisk together the egg and milk. Brush this mixture over the top crust to achieve a golden finish.

Protect Edges: To prevent the edges from over-browning, cover them with aluminum foil or a pie crust shield.

Bake: Place the pie in the preheated oven and bake for 50-60 minutes, or until the crust is golden brown and the filling is bubbling.

Cool: Once baked, remove the pie from the oven and let it cool on a wire rack for at least 2 hours. This allows the filling to set properly.