Put a baking sheet on middle rack of oven and preheat oven to 425°F.
Whisk together flour, cinnamon, nutmeg, and salt, then whisk in brown sugar, breaking up any lumps. Gently toss pears with brown sugar mixture, lemon juice, and vanilla and let stand 5 to 15 minutes to macerate fruit.
Roll out 1 piece of dough (keep remaining disk chilled) on a lightly floured surface with a lightly floured rolling pin into a 13-inch round. Fit into a 9-inch pie plate. Roll out remaining piece of dough into a 13-inch round. Reserve scraps.
Transfer filling to shell. Dot with butter, then cover with pastry round. Trim edges, leaving a 1/2-inch overhang (reserve scraps). Press edges together to seal, then fold under. Lightly brush top crust with some of egg wash, then cut 3 (1-inch-long) vents.
Roll out dough scraps about 1/8 inch thick and cut out leaf shapes with cutters (or a knife). Arrange decoratively on top of pie, pressing gently to help them adhere. Lightly brush top crust and cutouts with some of egg wash and sprinkle with granulated sugar.
Bake pie on hot baking sheet 20 minutes. Reduce oven to 375°F and bake until crust is golden and filling is bubbling, 40 to 45 minutes more. Cool to warm or room temperature, 2 to 3 hours.