Heat oven to 400°F. Line a large baking sheet with parchment.
Melt butter in a skillet over medium heat. Add apples, both sugars, cinnamon, nutmeg, and salt.
Stir in lemon juice and flour. Cook, stirring, until the juices thicken and apples soften slightly, 5–7 minutes.
Remove from heat. Stir in vanilla and cool the filling to room temperature.
Whisk egg and milk to make an egg wash. On a lightly floured surface, unroll or roll dough to 1/8-inch thickness.
Cut 4 to 5-inch circles. Brush edges lightly with egg wash.
Spoon a heaping tablespoon of apple filling onto each circle. Fold over to form half-moons and crimp edges with a fork.
Cut a small vent on top of each pie. Arrange on the prepared sheet, spacing slightly.
Brush tops with more egg wash and sprinkle with coarse sugar.
Bake until deep golden and bubbling at the vents, 18–22 minutes. Cool 10 minutes before serving.