To make the pie crust: To a 2-cup liquid measuring cup, whisk together the sugar, vinegar and 2 tablespoons of hot water until the sugar dissolves. Whisk in 1/3 cup ice water and stir to melt ice; chill in freezer until very cold, about 10 minutes (do not let it freeze).


In a medium bowl, add the flour and salt; whisk. Using a box grater, grate the butter atop the flour. Break up the butter until it resembles pea-sized balls. Transfer to the freezer to chill for 5 minutes.

Create a well in the center, and pour in about 3/4 of the sugar/water mixture. Stir to combine. Using your fingers, smash the butter into the flour. Continue stirring until a large mass forms, adding more water, if needed.

Dump onto your work surface and knead a good 5 to 7 times until it becomes a disk. Cut the disk in two, shaping it into a round and flattening it; wrap each one and transfer to the fridge for at least 2 hours, ideally overnight.

To make the filling: Preheat oven to 350°F. In a medium bowl, add the blueberries, blackberries, sugar, ginger, lime juice, salt, and 2 tablespoons of flour. Toss everything together.

Beat egg and heavy cream in a small bowl until no streaks remain. Roll out pie dough on a lightly floured work surface to a 15x10" rectangle. Cut a thin border around dough to square off edges. Cut dough in half lengthwise and then in thirds crosswise to form six 5" squares (do your best! I didn't do a flawless job with this and it all worked out!). Brush edges with egg mixture, then mound about 2 teaspoons of blueberry filling in 1 corner of each square. Working with 1 square at a time, fold corner opposite filling up and over to create a triangle; press edges with a fork to seal.

Place on a parchment-lined baking sheet and brush with remaining egg mixture. Cut about a 1"-long slit in the center of each turnover. Bake until pastry is golden brown and juices run from slits, 35–45 minutes. Let cool on baking sheet until slightly warm.

To make the glaze: In a medium bowl, add the powdered sugar, vanilla and salt. While whisking, add a warm tablespoon of water at a time, until the glaze is thick and smooth.

Dip each turnover in the glaze and transfer them to a wire rack with a piece of parchment underneath until set.