In a large skillet, heat a tablespoon of oil over medium heat. Add the chopped onion and minced garlic, sautéing until the onion is translucent.
Sprinkle the flour over the onion and garlic mixture, stirring for about 1 minute to cook out the raw flour taste.
Gradually add the chicken broth and milk, whisking continuously to prevent lumps. Continue cooking until the mixture thickens (about 3-5 minutes).
Stir in the shredded chicken, frozen vegetables, thyme, paprika, salt, and pepper. Remove from heat and mix in the Monterey Jack cheese until melted and well incorporated.
Roll out half of the pie crust and fit it into a 9-inch pie dish. Pour the chicken mixture into the crust.
Roll out the second half of the crust and place it over the filling. Seal the edges by crimping with your fingers or a fork. Cut a few slits on the top for steam to escape.
Beat the egg in a small bowl and brush it over the top crust for a golden finish.
Bake in the preheated oven for 25-30 minutes, or until the crust is golden brown and the filling is bubbly.
Remove from the oven and let it sit for about 10 minutes before serving to allow the filling to set.
Notes
Serve slices of the pot pie on individual plates, garnished with a sprig of fresh thyme or parsley for a pop of color. Enjoy with a side salad for a complete meal!