Instructions

for the pie dough

Whisk ice water and sour cream together in bowl. Process flour and salt in food processor until combined, about 5 seconds. Scatter chilled butter over top and pulse until butter is size of small lentils, about 10 pulses. Drizzle half of sour cream mixture over top and pulse until incorporated, about 3 pulses; repeat with remaining sour cream mixture.
Pinch dough with your fingers; if dough feels dry and does not hold together, add 1 to 2 tablespoons more ice water and pulse until dough forms large clumps and no dry flour remains, 3 to 5 pulses.
Divide dough into 2 even pieces. Form each piece into 4-inch disk, wrap tightly in plastic wrap, and refrigerate for 1 hour.

for the filling

Meanwhile, place 3 cups blueberries in medium saucepan. Cook over medium heat, stirring and mashing occasionally with potato masher, until half of blueberries are broken down and mixture measures 1½ cups, about 12 minutes. Let cool to room temperature, about 20 minutes.
Remove 1 disk of dough from refrigerator and roll out between 2 large sheets of parchment paper or plastic wrap to 12-inch circle, about ⅛ inch thick. (If dough becomes soft and/or sticky, return to refrigerator until firm.) Remove parchment from 1 side of dough and flip onto 9-inch pie plate; peel off second layer of parchment. Working around circumference, ease dough into plate by gently lifting edge of dough with your hand while pressing into plate bottom with your other hand. Leave dough that overhangs plate in place; refrigerate until dough is firm, about 30 minutes.
Meanwhile, roll second disk of dough between 2 large sheets of parchment paper or plastic wrap to 12-inch circle, about ⅛ inch thick. Refrigerate, leaving dough between parchment sheets, until firm, about 30 minutes.

for the pie

Adjust oven rack to lowest position and heat oven to 400 degrees. Place shredded apple in center of dish towel. Gather ends together and twist tightly to drain as much liquid as possible. Transfer apple to large bowl and stir in cooked blueberry mixture, remaining 3 cups uncooked blueberries, tapioca, lemon zest, and salt until combined. Transfer blueberry mixture to chilled dough-lined pie plate and scatter butter over top.
Using 1¼-inch round cookie cutter, cut out single round in center of remaining 12-inch dough circle. Cut out 6 more rounds from dough, 1½ inches from edge of center hole and equally spaced around center hole. Loosely roll dough circle around rolling pin and gently unroll it onto filling.
Trim any overhanging dough to ½ inch beyond lip of plate, then pinch edges of top and bottom crusts firmly together. Tuck overhang under itself; folded edge should be flush with edge of plate. Crimp dough evenly around edge of plate using your fingers. Brush surface with beaten egg white.
Set pie on aluminum foil–lined baking sheet and bake until crust is light golden brown, about 25 minutes. Reduce oven temperature to 350 degrees, rotate sheet, and continue to bake until juices are bubbling and crust is deep golden brown, 30 to 40 minutes longer. Let pie cool on wire rack until juices have thickened, about 2 hours. Serve.