Make the apple filling. Melt the butter in a medium saucepan over medium heat. Stir in the diced Granny Smith and Honey Crisp apples along with the granulated sugar, brown sugar, cinnamon, and lemon juice. Cook for 5–7 minutes, until the apples are just tender and the mixture is slightly thickened. Remove from the heat and let the filling cool.
Prep the crusts. Preheat the oven to 400°F. Line a baking sheet with parchment paper. Roll out the pie dough and cut into circles about 4–5 inches wide using a cookie cutter or the rim of a glass.
Assemble the pies. Spoon a small amount of the apple filling into the center of one dough circle. Place another circle on top and press around the edges to seal. Use a fork to crimp the edges so none of the filling escapes while baking. Brush the tops with the beaten egg, then cut two small slits in each pie to vent steam.
Bake. Arrange the hand pies on the prepared baking sheet and bake for 20–25 minutes, until golden brown. Let them cool on the pan for about 10 minutes.
Add the glaze. In a small bowl, whisk together the powdered sugar, milk, and vanilla until smooth. Drizzle over the cooled pies and let the glaze set before serving.