Roll out the dough to ⅛” thick and at least 1″ wider than a 9-inch pie plate. Place one portion into the pie plate, letting the edges hang over. Wrap and chill for 30 minutes.
Roll the second dough portion to the same size, place it on a parchment-lined baking sheet, cover, and chill for 30 minutes.
Preheat the oven to 500°F, placing a baking sheet or stone on the lowest rack.
Sprinkle oats on the bottom of the dough-lined pie plate to absorb moisture.
Mix sugars, flour, salt, spices, melted butter, and vanilla in a bowl. Toss with apple slices until evenly coated.
Spread the apple mixture over the oats, slightly mounding in the center.
Cover with the second dough, seal edges, flute, and cut slits for steam.
Brush the top with egg white, bake at 425°F for 25 minutes, reduce to 375°F, and bake for 35–40 minutes. Cool for at least 2 hours before slicing.