Preheat oven to 400 degrees.
Lightly grease a muffin pan.
Roll out the pie dough and cut circles slightly larger than the muffin cups.
Heat a large skillet over medium heat.
Add butter and cook the onion for 3 to 4 minutes until softened.
Add garlic and cook for 30 seconds.
Add carrots and celery.
Cook for about 5 minutes until the vegetables begin to soften.
Sprinkle in the flour and stir continuously.
Cook for 1 minute to remove the raw flour taste.
Slowly pour in the chicken broth while stirring constantly.
Add the heavy cream and continue stirring until smooth.
Season with salt, black pepper, garlic powder, onion powder, and thyme.
Simmer until the mixture thickens.
Add the shredded chicken and frozen peas.
Cook for 3 to 4 more minutes until the filling is creamy and thick.
Remove from heat and allow to cool slightly.
Press dough circles into the muffin cups.
Fill each cup with the chicken mixture.
Top with a second dough round and seal the edges.
Whisk the egg with a splash of water to make an egg wash.
Brush the tops with egg wash.
Bake for 20 to 25 minutes until golden brown and flaky.
Allow the pot pies to rest for 10 minutes before removing from the pan.
Serve warm.