Preheat the oven to 375°F (190°C).
Sauté the diced onions in butter over medium heat until translucent.
Add in the flour and stir to create a roux, cooking for about 1-2 minutes.
Slowly add the chicken broth while stirring, followed by the milk, and cook until thickened.
Stir in the shredded chicken, frozen vegetables, garlic powder, salt, and black pepper.
Roll out the pie crust and cut into circles to fit into muffin tin cups.
Press the circles of pie crust into the muffin tin and fill with the chicken mixture.
Top each filled crust with another circle of pie crust or create a decorative lattice overlay.
Brush the tops with the beaten egg for a glossy finish.
Bake for 25-30 minutes until golden brown.
Allow to cool for 5 minutes before removing from the muffin tin.