Make the crust: Whisk together flour, sugar, salt, and baking powder in a bowl. Cut in butter until it resembles coarse meal with several pea-size pieces remaining. Add ¾ cup milk, 1 tablespoon at a time, using a fork to pull dough together into a crumbly pile. (Add up to an additional 4 tablespoons of milk if needed.) Wrap dough in plastic wrap, using the plastic to flatten and press dough into a disk. Refrigerate until firm, 2 hours.

Make the filling: Meanwhile, whisk together granulated sugar, brown sugar, cornstarch, nutmeg, cinnamon, and salt in a bowl. Combine apples and ½ cup water in a large Dutch oven. Bring to a boil over medium-high heat. Add dry ingredients and stir to combine. Cook over medium-low, stirring occasionally, until thickened and apples are tender, 10 to 12 minutes. Stir in lemon extract. Cool to room temperature.

Line a baking sheet with parchment paper. On a floured work surface, roll dough to ⅛-inch thick. Use a 5-inch round cookie cutter to cut out circles. Reroll and cut scraps once. Scoop a scant ¼ cup filling in the center of each circle. Fold dough over filling, creating a half-moon shape, and crimp edges with a fork to seal. Place on prepared baking sheet and chill 15 minutes.

Set a wire rack in a rimmed baking sheet. Heat oil in a large Dutch oven, with a deep-fry thermometer attached, to 350°F. Fry pies, in batches, turning once, until golden brown, 2 to 3 minutes. Drain on prepared wire rack. Serve warm or at room temperature.