Make the crust: Pulse the flour, sugar and salt in a food processor. Add the butter and pulse until the mixture looks like coarse meal with pea-size bits of butter. Add 1/2 cup ice water and pulse until the dough just starts to come together. Divide the dough between 2 pieces of plastic wrap and form each into a disk; wrap tightly and refrigerate until firm, at least 1 hour.
Make the filling: Toss the peaches in a bowl with 3/4 cup sugar, the flour, lemon juice and spices.
Lightly dust a large piece of parchment paper with flour. Roll out 1 piece of the dough into a 12-inch round on the parchment. Ease the dough into a 9-inch pie plate. Add the filling, mounding it slightly in the center; dot with the butter and refrigerate. Roll out the second piece of dough into a 12-inch round and cut it into 1/2-inch-wide strips. Lay half of the strips on the pie in one direction, leaving about 1 inch of space between each strip. Lay the remaining strips on top, crossing them diagonally to make a lattice pattern (no need to weave); trim the edges of the strips, leaving a small overhang. Fold the overhanging dough under itself and crimp the edge of the crust with your fingers.
Beat the egg with 1 tablespoon water and brush on the crust edge and lattice top. Sprinkle with the remaining 1 tablespoon sugar and refrigerate until firm, about 30 minutes.
Position a rack in the lower third of the oven. Put a baking sheet on the rack and preheat to 425 degrees F. Put the pie on the hot baking sheet and bake 20 minutes. Reduce the oven temperature to 375 degrees F and continue baking until the pie is golden and the filling is bubbly, 50 minutes to 1 hour. (Cover loosely with foil if the top is browning too quickly.) Transfer to a rack to cool completely before slicing.