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For the filling:
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Preheat oven to 425F.
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Add 2 1/4 teaspoons of oil in a large skillet or Dutch oven over medium heat.
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Add leeks and carrots and cook, stirring, until the leeks soften, 6 to 8 minutes.
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Stir in garlic and cook, stirring, 1 minute more.
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Add wine and stir until most of the liquid has evaporated.
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Stir in flour and sage and cook, stirring frequently, until the flour begins to change into light brown, 1 to 3 minutes.
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Add broth and bring to a simmer, stirring constantly, until the sauce thickens and the carrots just start tender, 4 to 6 minutes.
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Stir in turkey and peas and season to taste with salt and pepper.
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Remove from heat and transfer the mixture to a deep 10-inch pie pan or other 2-quart baking dish and set aside.
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For the mashed potatoes:
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Put potatoes in a large saucepan covered with cold water.
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Bring to a boil over medium heat.
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Cook, partially covered, until the potatoes are tender, 9 to 11 minutes.
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Drain well and return the potatoes to the pan.
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Cover and shake the pan over low heat to dry the potatoes slightly, 1 to 2 minutes.
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Remove from the heat.
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Mash the potatoes with a potato masher, fork or whip with an electric mixer, adding enough buttermilk to make a smooth puree.
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Season with salt and pepper.
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Mix in egg and 1/2 tablespoon oil.
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Spread the potatoes evenly on top of the turkey mixture.
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With the back of a spoon, make decorative swirls.
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Arrange the baking dish on a baking sheet and bake until the potatoes and filling are heated through and the top is golden brown, 28 to 30 minutes.
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Cool for about 5 minutes.
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Serve warm.