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1
Place a baking sheet in the oven and preheat to 400 degrees F. Line a 9-inch pie plate with 1 piece of dough; refrigerate until ready to assemble.
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2
Make the cinnamon-roll crust: Lay the remaining piece of dough on a lightly floured surface and spread the butter evenly on top.
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3
Combine 1/4 cup granulated sugar and 1 teaspoon cinnamon in a small bowl; sprinkle evenly over the butter, then gently press with your fingers to help the mixture adhere.
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4
Roll the pie dough into a tight log.
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5
Trim and discard about 1 1/2 inches from both ends; cut the remaining log crosswise into 1/2-inch-thick pieces.
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6
Arrange the pieces cut-side down in a snug circle on floured parchment paper.
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7
Lightly dust with more flour, then gently roll out into a 10-inch round.
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8
Slide the parchment onto a baking sheet and refrigerate until ready to assemble the pie.
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9
Peel and thinly slice the apples.
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10
Toss with the lemon juice, vanilla and the remaining 1/4 cup granulated sugar and 1/8 teaspoon cinnamon in a large bowl.
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11
Transfer to the dough-lined pie plate; invert the cinnamon-roll crust on top and peel off the parchment (it's OK if the individual rounds separate a bit in the process).
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12
Pinch the crusts together; fold the overhanging dough under itself and crimp as desired.
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13
Brush with the beaten egg.
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14
Set the pie on the hot baking sheet in the oven; bake until the crust is golden brown and the filling is bubbling, about 50 minutes.
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15
(Tent loosely with foil if the top browns too quickly.)
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16
Transfer to a rack to cool slightly.
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17
Whisk the confectioners' sugar and 2 tablespoons milk in a bowl until smooth.
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18
(Add more milk if the glaze is too thick.)
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19
Drizzle over the pie.
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20
Photograph by Levi Brown
