Number 1 tip: keep EVERYTHING as cold as possible. Chill crust ingredients (yes even the flour!) before starting and keep the peaches/filling as cold as possible right up until going into the oven.
CRUST: To make the crust, sift together the flour, sugar, and salt in a medium bowl. Cut in the shortening with a pastry blender until the mixture resembles large peas. Whisk together the ice water, vinegar, and egg in a small bowl. Add the egg mixture to the flour mixture and stir with a fork until just combined. Divide the dough in half; flatten each half into a disk and wrap in plastic wrap. Chill for 2 hours or up to overnight.
OVEN PREP: Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
CRUST CONT.: Roll out one dough disk on a lightly floured surface to form a round, about 1/4-inch thick. Fit the dough into a 9-inch pie plate. Roll out the other dough following the same procedure. Place the second round of dough on the prepared baking sheet. Cut it into 2-1/2 inch-wide strips. Chill the dough while preparing the filling.
FILLING: Prepare the peaches (See Note 1). To make the filling, place the prepared peaches in a large bowl. Add the lemon juice and vanilla and gently toss to combine. In a separate bowl, stir together the 1/2 cup sugar, the cornstarch, and salt. Add to the peaches and gently toss to combine.
ASSEMBLY: Spoon the filling into the dough-lined pie plate. Arrange the pastry strips on the top of the pie in a lattice. Fold the edges under and crimp. Beat the egg and 1 tablespoon water together in a small bowl. Brush the egg wash lightly over the top crust. Sprinkle with the 1 tablespoon sugar. Chill pie for 20 minutes.
BAKE: Line a baking sheet with aluminum foil and place it on the bottom rack of the oven (to catch any filling that bubbles over). Bake the pie on the center rack for 15 minutes. Reduce the oven temperature to 375 degrees F and bake for 40 to 50 minutes more, until golden brown and bubbling, shielding the pie with a sheet of foil after 20 minutes if the crust is getting too brown. Let cool completely on a wire rack, about 2-4 hours, or until thickened and set, before slicing and serving.