In a mixing bowl, combine the flour and cold, cubed butter. Use a pastry cutter or fingertips to mix until the mixture resembles coarse crumbs with pea-sized pieces. Gradually add ice water a tablespoon at a time, mixing until the dough begins to come together. Form the dough into a disc, wrap in plastic wrap, and refrigerate for 30 minutes.
1 ¼ cups all-purpose flour, ½ cup unsalted butter, 3-4 tablespoons ice water
Preheat your oven to 375°F (190°C). Remove the chilled dough from the refrigerator. On a lightly floured surface, roll the dough out into a 12-inch circle. Transfer it to a 9-inch pie dish, trimming any excess crust hanging over the edges. Crimp the edges decoratively and set aside.
1 ¼ cups all-purpose flour, ½ cup unsalted butter
In a saucepan, combine the berries, ½ cup sugar, cornstarch, vanilla extract, and a pinch of salt. Cook over medium heat, stirring constantly, until the mixture thickens and bubbles, about 5-7 minutes. Remove from heat and let cool slightly.
3 cups mixed berries (strawberries, blueberries, raspberries), ¾ cup granulated sugar, 3 tablespoons cornstarch, 1 teaspoon vanilla extract
Pour the warm berry filling into the prepared pie crust, spreading evenly. Dot the filling with small pieces of butter if desired for extra richness. Roll out a second circle of dough or cut strips for a lattice top, and place over the filling. Trim and crimp the edges to seal.
Create an egg wash by whisking together the egg yolk and water. Brush the top crust with the egg wash to give it a shiny, golden finish. Make a few small slits in the top crust to allow steam to escape.
1 egg egg yolk, 1 tablespoon water
Bake the pie in the preheated oven for approximately 40 minutes, or until the crust is golden brown and the filling is bubbling through the vents. Remove from the oven and let cool for at least 2 hours to set before slicing.