2-1/2 cups all-purpose flour (spooned and leveled) plus more for rolling
1 teaspoon salt
1 teaspoon sugar
1 cup (2 sticks) cold unsalted butter, cut into pieces
2 cups mixed fresh berries, such as blueberries, raspberries, strawberries (quartered lengthwise), and blackberries (halved if large)
½ cup granulated sugar
2 tablespoons cornstarch
juice of ½ a lemon, about 4 tsp
eggwash: 1 egg beaten with 1 T water
sanding sugar or granulated sugar to garnish, optional
Prepare dough: In a food processor, combine flour, salt, and sugar; pulse to combine. Add butter; pulse until mixture resembles coarse meal, with just a few pea-size pieces of butter remaining. Sprinkle with 4 tablespoons ice water. Pulse until dough is crumbly but holds together when squeezed with fingers (if necessary, add up to 4 tablespoons more ice water, 1 tablespoon at a time). To help ensure a flaky crust, do not overprocess.
Transfer half of the dough (still crumbly) onto a piece of plastic wrap. Form into a square 3/4 inch thick; wrap tightly in plastic. Repeat with the other half. Refrigerate until firm, at least 1 hour (and up to 3 days).
Prepare filling: In a medium bowl, toss together berries, granulated sugar, cornstarch, and lemon juice.
Preheat the oven to 425. On a lightly floured surface, roll first disk out to an 8 x 12-inch rectangle. Cut into six 4-inch squares. Spoon berry mixture into the center of each square. Brush 2 opposite sides of each square with egg wash and fold into triangles. Crimp edges to seal. Transfer to a parchment paper-lined baking sheet. Repeat with second dough. Brush tops with eggwash. Sprinkle with sugar if desired and make a ½ inch incision to create a steam vent in the middle of each of triangle. Bake until golden brown and crisp, 20 to 25 minutes, rotating sheet pan halfway through.