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Preheat oven to 425.
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Place potatoes and carrots in medium saucepan; add water to cover.
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Bring to a boil. Reduce heat, cook covered, 8-10 minutes or until crisp-tender. (Check after about 5 minutes. These cook pretty fast and you don't want them to get mushy.) Drain.
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In a large skillet, heat butter over medium-high heat.
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Add onion. Cook and stir until tender.
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Stir in flour and seasonings until blended.
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Gradually stir in broth and milk. Bring to a boil, stirring constantly. Cook and stir 2 minutes or until thickened.
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Stir in chicken, peas, corn and the potato mixture. Remove from heat.
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Unroll a pastry sheet into a 9-inch pie plate. Trim even with rims.
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Add chicken mixture.
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Unroll remaining pastry sheet and place over the filling. Trim, seal and flute edges. Cut slits in the top.
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Bake 35-40 minutes or until crust is lightly browned. (I usually check it around 25 minutes to make sure the edges aren't getting too dark. With my oven, the back side browns faster so I rotate it after 25 minutes.)
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Let it stand 15 minutes before cutting (if you can wait that long).