Prepare an ice-water bath and bring a large pot of water to a boil. Cut an X in flower (non-stem) end of each peach. Drop in boiling water and cook just until skins begin to peel back, about 30 seconds. Transfer to ice-water bath, then peel and pit peaches. Cut into ½-inch wedges (you should have 7 to 8 cups).

In a large bowl, stir together sugar and vanilla seeds, then add peaches, lemon juice, and salt; stir to combine. Let stand 30 minutes, then stir in cornstarch. Set a colander over a heatproof bowl; transfer peaches to colander to drain. Transfer liquid in bowl to a small saucepan, then transfer peaches to bowl. Bring liquid to a boil over medium-high heat, then cook, whisking constantly, until thickened to the consistency of loose pudding, 1 to 2 minutes. Stir into peaches; let stand 15 minutes.

On a lightly floured surface, roll out smaller piece of dough into a 13-inch round, about ⅛ inch thick. Fit into a 9-inch pie dish. Fill with peach mixture. Roll larger piece of dough out into an approximately 12-by-16-inch rectangle, a scant ⅛ inch thick. Using a pastry wheel or large knife, cut into 1 ½-to-2-inch-wide strips.

Place 6 strips atop pie, leaving a little space between them. Fold back every other strip, and lay a strip across center of pie, perpendicular to original strips. Unfold folded strips, then fold back remaining strips. Lay another horizontal strip across pie. Repeat folding and unfolding strips to weave a lattice pattern. Repeat on remaining side. Press edges together to seal. Trim dough to a 1-inch overhang, fold under, and crimp as desired. Refrigerate 15 minutes.

Preheat oven to 400°F.

Brush top of chilled pie with beaten egg.

Place on middle rack of oven and slide a baking sheet or a piece of aluminum foil onto rack below to catch any overflow. Bake 15 minutes, then reduce temperature to 375°F and bake until bubbling in center and top and bottom crusts are browned, about 1 hour, 30 minutes more.

Let cool completely on a wire rack, at least 4 hours. Pie is best eaten the day it's made, but can be stored, lightly covered, at room temperature, up to 2 days.