To make the crust: Prepare the dough as directed, dividing it into two pieces: 2/3 for the bottom crust and 1/3 for the lattice top. Roll out the larger piece and line a 9″ deep-dish pie pan.
Chill the lined pan in the refrigerator. Roll out the second piece and cut 1 1/2″ strips for a lattice top. Weave the lattice on a parchment circle, place on a plate, and refrigerate.
To make the filling: Squeeze the grapes to separate flesh from skin. Reserve the skins. Simmer the pulp in a 2-quart saucepan until it breaks into juice, about 10 minutes. Strain through a sieve to remove seeds, pressing to extract juice.
Cool the grape mixture. Whisk together sugar, cornstarch, and salt. Stir into the grape mixture along with the vanilla.
Fill the pie crust with grape filling and cover with the lattice top. Brush with beaten egg and sprinkle with sugar.
Bake in a preheated oven at 375°F (190°C) until the crust is golden and the filling is bubbly, about 45-50 minutes.