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1
Preheat oven to 400F.
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2
Place chicken on a rimmed baking sheet; season both sides with salt and pepper.
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3
Roast until an instant-read thermometer inserted in thickest part of breasts (avoiding bone) registers 165F, 25 to 30 minutes.
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4
Let cool slightly; remove skin and bones, and shred meat.
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5
While chicken is roasting, heat 2 tablespoons oil in a large saucepan over medium.
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6
Add carrots, onion, and thyme; season with salt and pepper.
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7
Cook until carrots are tender, stirring occasionally, 8 to 10 minutes.
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8
Add flour; cook, stirring, 1 minute.
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9
Gradually add milk, whisking until smooth.
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10
Cook, stirring occasionally, until mixture comes to a simmer and thickens, about 6 minutes.
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11
Remove from heat; stir in peas, lemon juice, and chicken, and season with salt and pepper.
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12
Pour filling into a 9-inch round baking dish or deep-dish pie plate.
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13
Stack phyllo on a work surface.
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14
Using a plate or pot lid as a guide, cut an 11-inch round from the stack with a paring knife; discard trimmings.
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15
Stack two rounds on work surface, and brush gently with 1 teaspoon oil; top with another two rounds, and brush with 1 teaspoon oil.
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16
Repeat with remaining two rounds and 1 teaspoon oil.
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17
Place stacked phyllo over filling, and press down about 1/2 inch from the edge so phyllo fits inside rim of baking dish, with edges sticking straight up around rim.
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18
Bake until crust is lightly golden and filing is bubbling, 20 to 25 minutes.
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19
Let cool 15 minutes before cutting and serving.
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20
Phyllo dough is usually sold in 1-pound packages, which each contain about 20 sheets of dough.
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21
Thaw in original box in the refrigerator (check the label for instructions), and do not unwrap until ready to use.
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22
Leftover phyllo can be wrapped tightly in plastic and stored in a resealable plastic bag; refrigerate up to 1 week or freeze up to 2 months.