Cook 1 lb. peaches (about 4), peeled, cut into ¼” pieces, or 1 lb. frozen, slightly thawed peaches cut into ¼” pieces, ⅓ cup granulated sugar, 1 tsp. finely grated lemon zest, 1 tsp. fresh lemon juice, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt in a medium heavy saucepan over medium-low heat, stirring occasionally with a heatproof rubber spatula, until peaches are softened, juices are thickened, and mixture resembles a chunky jam, 45–60 minutes. Let cool.
Do ahead: Filling can be made 1 week ahead. Cover and chill.
Dough and Assembly
While the peaches are cooking, whisk 2 tsp. granulated sugar, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 2½ cups (313 g) all-purpose flour in a large bowl until combined. Using a pastry cutter or your fingers, work in ½ cup (1 stick) chilled unsalted butter, cut into 1″ pieces, until largest pieces are pea-size. (Alternatively, pulse together dry ingredients in a food processor, then pulse in butter.) Sprinkle 2 Tbsp. apple cider vinegar over and mix with your hands to combine. Drizzle ¼ cup plus 3 Tbsp. ice water over and mix by hand until dough just comes together in a shaggy mass.
Turn out dough onto a lightly floured surface and gather into a ball. Divide in half and pat into disks; wrap each in plastic. Chill at least 15 minutes.
Working one disk at a time, unwrap dough and roll out on a lightly floured surface to ⅛” thick. Using a 5″-diameter cutter or bowl, punch out as many rounds as you can, transferring to a baking sheet as you go. Gather dough scraps, reroll, and punch out more rounds. (You should get 12 or 13 in all.)
Working with 1 round at a time, spoon a heaping tablespoonful of filling onto 1 side. Brush edges with water, then fold empty side of dough up and over filling and bring edges together to create a half-moon shape. Crimp edges firmly with a fork to seal. Arrange pies on a parchment-lined baking sheet and chill until firm, about 15 minutes.
Fit a large heavy skillet, preferably cast iron, with thermometer and pour in vegetable oil to come ½” up sides. Heat over medium-high until thermometer registers 340°.
Working in 3 or 4 batches, keeping remaining pies chilled until ready to fry, and adding more oil between batches if needed, fry pies, turning every 2 minutes with tongs and adjusting heat as needed to maintain oil temperature, until golden brown and crisp, 13–15 minutes; if you see any pies beginning to burst open toward the end of cooking, immediately remove from oil. Transfer to paper towels to drain.
Just before serving, transfer pies to a platter and dust with powdered sugar.
Do ahead: Dough can be made 1 day ahead. Keep chilled.