Make the pie dough: In a medium bowl, whisk together ¼ cup plus 2 tablespoons ice cold water, the balsamic vinegar, and the egg. Transfer to the fridge to keep cold.
In a large bowl, whisk together the all-purpose flour, rye flour, sugar, and salt. Add the butter and, using your fingers or a pastry blender, rub the butter into the flour mixture until it resembles coarse breadcrumbs with a few pea-sized pieces. Retrieve the liquid mixture from the fridge and gradually drizzle it into the flour mixture, stirring lightly with a fork until a shaggy dough just clings together. (Stir in an additional 1–2 tablespoons of cold water if the dough feels dry.). Gather the dough together, divide it evenly in half, and press into two disks. Wrap each disk tightly in plastic wrap and refrigerate until firm, at least one hour.
Make the filling: In a heavy medium pot, stir together the cherries, lemon juice, cane sugar, brown sugar, cornstarch, bitters, vinegar, vanilla bean seeds, and salt. Set aside to macerate for 15 minutes, then set over medium-low heat and bring to a boil, stirring frequently to prevent sticking. Lower the heat to low and cook, stirring frequently, just until the mixture thickens and the cherries soften but still hold their shape, about 8 minutes. Transfer to a heatproof bowl, set aside to cool to room temperature, then cover and refrigerate until you are ready to assemble the pies.
Line a large rimmed baking sheet with parchment paper and set it aside. Lightly flour a clean work surface. Retrieve one disk of dough from the fridge and, using a rolling pin, roll the dough out to an even ⅛-inch thickness. Using a 6-inch round cutter or a similarly-sized bowl and a paring knife, Cut out four circles of the dough, saving the scraps. Transfer the circles to the lined baking sheet, then repeat with the second disk of dough.. Combine the scraps and reroll once to get 1 or 2 additional circles. Refrigerate the circles until firm, at least 30 minutes.
Retrieve the filling and pastry circles. Place 2 tablespoons of the filling on one half of each circle, leaving a ½-inch border. Brush the edges of the circles lightly with the egg wash, then fold the dough over to cover the cherries and form a half-moon shape. Using the tip of a chopstick or the tines of a fork, press the edges to seal and crimp. Repeat with the remaining pastry circles. Use a small fork or a paring knife to poke steam vents in the top of each pie, brush lightly with egg wash, and sprinkle with additional raw sugar. Transfer to the freezer and freeze until the dough is firm, at least 30 minutes. (If assembling more than 3 hours before baking, cover tightly with plastic wrap.)
Preheat the oven (with one of its racks positioned in the center) to 375°F. Transfer the chilled pies to the oven and bake until the crust is deeply golden and the juices bubble up from the center, 25–30 minutes. Cool slightly on the baking sheet, then use an offset spatula to loosen the pies from the parchment paper. Serve warm or at room temperature. Cooled pies may be transferred to an airtight container and stored at room temperature for up to two days.