In a bowl, combine 2 1/2 cups flour and salt. Cut in 1 cup butter until mixture resembles coarse crumbs. Stir in water, one tablespoon at a time, until mixture forms a ball. Divide into two balls and wrap in plastic, refrigerating for at least 4 hours.
Position oven rack in bottom third of oven and preheat to 400 Degrees F. Combine 3/4 cup sugar and vanilla bean in processor; blend until vanilla bean is finely minced. Sift vanilla sugar through strainer into bowl; discard any large pieces. Mix 4 tablespoons flour and nutmeg into vanilla sugar. Add peaches to mixture and toss to coat.
Take 1 of the 2 dough balls and roll out to fit a 9 inch pie plate. Place dough in pie plate. Press the dough evenly into the bottom and sides of pie plate. Spoon peach filling into dough; dot with 1/3 cup butter. With the other dough ball, create a lattice for top of pie. Brush top of pie with egg and sprinkle 3 teaspoons of sugar on top.
Place pie on rimmed baking sheet. Bake for 1 hour until peaches are tender, crust is golden brown and juices are bubbling through lattice. Transfer pie to rack and cool.