Cinnamon Bun Apple Pie

Directions

1. 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.
2. 2
   Make the cinnamon-roll crust: Lay the remaining piece of dough on a lightly floured surface and spread the butter evenly on top.
3. 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.
4. 4
   Roll the pie dough into a tight log.
5. 5
   Trim and discard about 1 1/2 inches from both ends; cut the remaining log crosswise into 1/2-inch-thick pieces.
6. 6
   Arrange the pieces cut-side down in a snug circle on floured parchment paper.
7. 7
   Lightly dust with more flour, then gently roll out into a 10-inch round.
8. 8
   Slide the parchment onto a baking sheet and refrigerate until ready to assemble the pie.
9. 9
   Peel and thinly slice the apples.
10. 10
    Toss with the lemon juice, vanilla and the remaining 1/4 cup granulated sugar and 1/8 teaspoon cinnamon in a large bowl.
11. 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).
12. 12
    Pinch the crusts together; fold the overhanging dough under itself and crimp as desired.
13. 13
    Brush with the beaten egg.
14. 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.
15. 15
    (Tent loosely with foil if the top browns too quickly.)
16. 16
    Transfer to a rack to cool slightly.
17. 17
    Whisk the confectioners' sugar and 2 tablespoons milk in a bowl until smooth.
18. 18
    (Add more milk if the glaze is too thick.)
19. 19
    Drizzle over the pie.
20. 20
    Photograph by Levi Brown