Melt butter in a medium saucepan over medium heat.
Add diced apples, sugars, cinnamon, and lemon juice. Cook for 5-7 minutes until apples soften slightly. Remove from heat and let cool.
Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Roll out the pie crust and cut circles about 4-5 inches wide.
Place a spoonful of apple filling in the center, cover with a second dough circle, and press edges to seal.
Crimp with a fork, brush with beaten egg, and cut two small slits on top.
Bake for 20-25 minutes until golden brown. Let them cool slightly.
Mix powdered sugar, milk, and vanilla.
Drizzle over cooled pies and let set.