In a large saucepan, heat the olive oil over medium heat. Add the diced onion and minced garlic; sauté for about 3-4 minutes until the onion is translucent.
Stir in the shredded chicken and frozen mixed vegetables, cooking for an additional 3-4 minutes.
Pour in the chicken broth and bring to a gentle simmer. Add thyme, rosemary, salt, and pepper. Simmer for 5-7 minutes.
Stir in the heavy cream and simmer for another 5 minutes. If desired, mix cornstarch with cold water to form a slurry and stir it in, cooking until thickened.
Set the filling aside to cool slightly while preparing the pie crust.
Roll out one pie crust to fit a 9-inch pie dish. Pour the chicken filling into the prepared crust.
Place the second pie crust over the filling. Seal the edges by crimping them together. Cut slits in the top crust for steam to escape.
Beat the egg and brush it over the top crust.
Bake for 25-30 minutes until the crust is golden brown and the filling is bubbling.
Let the pot pie cool for about 10 minutes before serving.
Notes
Serve warm, garnished with fresh thyme leaves for an added touch.