In a large skillet over medium heat, add olive oil. Sauté the chopped onion, garlic, carrots, and potatoes for about 5-7 minutes until they start to soften.
Stir in the shredded chicken, peas, thyme, salt, and pepper. Cook for another 2-3 minutes.
Pour in the chicken broth and heavy cream. Stir to combine, bringing the mixture to a simmer. Let it cook for 5-7 minutes until the sauce thickens. Remove from heat and let it cool slightly.
Preheat the oven to 425°F (220°C).
Roll out one pie crust and fit it into a 9-inch pie dish. Pour the chicken mixture into the crust. Roll out the second crust and place it on top. Seal the edges by crimping them together. Cut a few slits in the top crust for steam.
Brush the top crust with the beaten egg for a golden finish.
Place the pot pie in the preheated oven and bake for 30-35 minutes, or until the crust is golden brown and the filling is bubbling.
Allow the pie to cool for about 10 minutes before slicing.
Notes
Let the pie cool for a few minutes before slicing to allow the filling to set.