Preheat the oven to 425°F (220°C).
In a large saucepan, melt the butter over medium heat.
Add the chopped onions to the butter and sauté until translucent, about 3-4 minutes.
Stir in the flour and cook for another 1-2 minutes.
Gradually whisk in the chicken broth and milk until the mixture is smooth.
Add the shredded chicken, frozen vegetables, garlic powder, dried thyme, salt, and pepper.
Remove the saucepan from the heat and let the filling cool slightly while you prepare the crusts.
Roll out one pie crust and place it in the bottom of your muffin tin or ramekins.
Spoon a generous amount of the chicken filling into each crust.
Roll out the second pie crust and place it over the filling, sealing the edges gently.
Cut a few slits in the top crust to allow steam to escape.
Brush the top of each pie with beaten egg for a golden finish.
Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown.
Allow the mini pot pies to cool for a few minutes before serving.