Preheat the oven to 425°F. Place the potatoes and carrots in a large saucepan, and add enough water to cover the vegetables. Bring the water to a boil. Then, reduce the heat. Cook, covered, for 8 to 10 minutes or until the veggies are crisp-tender. Drain and discard the water.
In a large skillet, heat the butter over medium-high heat. Add the onion. Cook and stir until the onion is tender. Stir in the flour and seasonings until blended.
Gradually stir in the broth and milk. Bring the mixture to a boil, stirring constantly. Cook and stir for two minutes or until the mixture is thickened. In a large bowl, combine the chicken, peas, corn, and potato-carrot mixture. Stir in the broth mixture.
Unroll a pie crust into each of the two 9-inch pie plates. Trim the crusts even with the rims of the plates. Add half the filling to each pie plate.
Unroll the remaining pie crusts. Working with one pie crust at a time, place it over the filling in each pie plate. Trim, seal and flute the edges. Cut a few slits in the tops. Editor's Tip: To seal the pie, roll the edges of the top and bottom pie crusts together. Then, to flute the edge, position your index finger on the outside edge of the pie, facing inward. Position your other hand's thumb and index finger on the inside edge, and gently press the crust into your outer index finger. Pinch to form a V. Continue around the pie crust until you reach the original flute.
Bake for 35 to 40 minutes or until the crust is lightly browned. Let the potpie stand for 15 minutes before cutting.