Preheat the oven to 400°F.
In a medium saucepan over medium heat, melt the butter.
Stir in the flour, onion powder, garlic powder, salt, and pepper, cooking for about 1 minute until bubbly.
Gradually whisk in the chicken broth and milk, cooking until the mixture thickens, about 3-5 minutes.
Stir in the shredded chicken and mixed vegetables, then remove from heat.
Roll out one pie crust and use a round cutter to cut out circles that will fit into your muffin tin.
Press the circles into the bottom of each muffin cup.
Fill each cup with the chicken mixture, then top with another round of pie crust, sealing the edges.
Cut small slits in the top crust for steam to escape.
Brush the tops with the beaten egg.
Bake for 20-25 minutes or until the crust is golden brown.
Allow to cool for a few minutes before serving.