Whisk the cornstarch and water together until all the cornstarch has dissolved. Place the berries, sugar, cornstarch mixture, and lemon juice into a small saucepan over medium heat. Stir the mixture as it cooks. Bring it to a simmer and allow to simmer for 3 minutes, stirring constantly. Remove pan from the heat and cool completely.
Whisk the flour, sugar, and salt together in a large bowl. Place the cold and cubed butter on top. Gently toss the flour and butter together with your hands, and then briefly rub the butter into the flour.
Begin adding the ice cold water 1 Tablespoon at a time until dough forms 1 large shaggy clump in your bowl. Use your hands to toss the mixture together after you add each Tablespoon.
Pour the shaggy clump of dough out onto a lightly floured work surface. Pat the dough down until it’s ¾ – 1 inch thick, about a 5×8 inch rectangle. Fold the dough into thirds. Wrap it up tightly and refrigerate for at least 2 hours.
Take the dough out of the refrigerator to begin the rolling and folding process. Roll the dough into a 6 inch wide and 12 inch tall rectangle that’s ½ inch thick. Fold the rectangle into thirds. Repeat rolling and folding 4 more times for a total of 6 times.
Wrap up/seal tightly and refrigerate for at least 15 minutes.
Line two large baking sheets with parchment paper. Roll dough into a 12-inch square. Cut into 9 4-inch squares. Transfer squares to prepared baking sheets.
Spoon 1 heaping Tablespoon of filling into the center of each square. Fold one corner over the filling to make a triangle. Crimp the edges of the turnovers together to seal.
Chill the shaped turnovers in the refrigerator for at least 15 minutes.
Preheat oven to 400°F (204°C). Whisk the egg and milk together. Brush on each turnover. Cut 3 slits into the tops of each to allow steam to escape.
Bake for 22-25 minutes or until golden brown on top and around the edges. Remove baked turnovers from the oven. Cool for at least 5 minutes before icing/serving. Drizzle with vanilla icing if desired.
