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Preheat the oven to 375°F.
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Spoon the chicken mixture into a 1 1/2-quart baking dish.
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Roll out the sheet of puff pastry into an 11-inch-square.
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Drape the puff pastry over the pie and press it against the rim of the dish to seal.
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Cut slits into the pastry to allow steam to escape.
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Mix the egg and remaining 1 tablespoon of milk in a small bowl to blend.
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Brush some of the egg mixture over the pie and garnish with sesame seeds.
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Set the pie on a heavy baking sheet and bake for 50 minutes, or until pastry is golden brown.
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Set aside for 30 minutes to cool slightly.