Preheat the oven to 425.
Boil the potatoes and carrots in a large saucepan over medium heat until almost tender., about 10 minutes.
Drain and set aside. In a large skillet, saute the onion and butter until tender.
Stir in the flour, salt, pepper, and chicken soup base until blended.
Gradually stir in the broth and milk. Cook, stirring for 2 minutes or until thick.
Add the chicken, peas, potatoes, and carrots to the broth mixture.
Remove from the heat.
Divide the chicken mixture evenly between two unbaked pie shells.
Use some water to wet rim of the bottom crusts which will help both crusts adhere together.
Cover the pies with the top crusts, crimping the crusts together all the way around.
Bake the pies for 35 to 40 minutes until the crust is golden brown.
Cool on a wire rack or windowsill until the pie is firm, about 45 minutes.
Pie will keep for a week sealed in the refrigerator.