Preheat oven to 400°F. Line a large baking sheet with parchment paper.
Cook cherries, sugar, cornstarch, salt, and lemon juice in a saucepan over medium heat, stirring until thick and glossy, 5–7 minutes.
Stir in almond and vanilla extracts and the butter. Let the filling cool 10 minutes.
Dust the counter with flour. Unroll dough and gently roll to even thickness.
Cut 16 rounds with a 4-inch cutter, re-rolling scraps as needed. Transfer half the rounds to the baking sheet.
Spoon about 1 to 1½ tablespoons filling onto centers. Brush edges with a little milk.
Top with remaining rounds, press to seal, and crimp edges with a fork. Cut a small vent on each pie.
Brush tops with remaining milk and sprinkle with coarse sugar. Bake until deep golden, 18–22 minutes.
Cool on the sheet 5 minutes, then move to a rack to finish cooling before serving.