Preheat the oven to 350°F with a rack in the center position.

Filling: Place the apples and butter in a glass bowl and microwave them, uncovered, for three minutes, until they've softened but still retain a bit of “bite.” Stir so that the butter coats the apple slices. In the meantime, whisk together the dry ingredients in a large bowl. Add the syrup and vanilla and stir until well-blended, then stir in the apples.

Line a 10-inch pie plate with one round of dough. Use a pastry brush or your fingertips to gently waterproof the inside of the pastry with egg white. Pile in the filling. Cut remaining dough into half-inch strips and weave a lattice-top. Seal and crimp the edges, trimming any excess. Stir together the egg yolk and milk, then brush it on the top. Sprinkle with sugar.

Baking: Place the pie on a parchment-lined baking sheet (to catch any spills), and bake for 90 minutes to two hours, until the top crust is golden brown and the filling is bubbly. Check periodically and add some foil or crust-protector over the edges if they’re getting too brown. Rotate the pie 180° mid-baking. Remove the pie from the oven and allow it to cool for at least two hours before cutting. May be stored for a day or so at room temperature, or covered and refrigerated for up to 5 days.