Preheat oven to 425F; place potatoes and carrots in a saucepan; add to enough to cover; bring to a boil; reduce heatl cook, covered 8-10 minutes; drain
In a skillet, heat butter over medium-high heat; add onion; cook and stir until tender; stir in flour and seasonings until blended; slowly stir in broth and milk; bring to a boil, stir constantly; cook and stir for 2 minutes until thick; stir in chicken, peas, corn and potato mixture; remove from heat
Unroll a pie crust into each of two 9 inch pie plates; trim even with rims; add chicken mixture; unroll remaining crusts; place over filling; trim and seal edges; cut slits in tops
Bake for 35-40 minutes until crust is lightly browned; let stand 15 minutes before cutting