This recipe yields two pies, so make half if you want only one pie. Bring a large pot of water to a boil, and cook the diced carrots and potatoes until cooked but firm. Drain and set aside.
In the same pot, melt the butter and saute the chopped onion. Add the flour and cook for about two minutes.
Whisk in the chicken broth and milk, and cook until thickened and the mixture coats the back of a spoon.
Add the cooked potatoes, carrots, frozen peas, and corn to the sauce.
Mix in the shredded chicken, dried thyme, salt, and pepper until well combined.
Let your mixture cool off for a while, and take out the refrigerated pie crusts to bring them to room temperature. Preheat oven to 425 F.
Line two pie dishes with a crust, and fill each with half of the chicken/ veggie mixture.
Top with the other two pie crusts and pinch the edges to seal. Make an egg wash ( one egg yolk beaten with a tbsp of water) and brush the pie crusts. Make four slits as if to divide the pie into 8 portions, and bake for 35-45 minutes until golden brown.