Preheat oven to 425°. Mix ¾ cup sugar and cornstarch together and toss with the berries and vanilla. Allow this mixture to sit for 30 minutes.
Place bottom crust into the pie pan and fill with the fruit mixture. Dot the top of the filling with butter. Next, choose a method for the top crust: 1. Place the second crust on top, making sure to seal edges; slash the top. 2. Use the second crust to create a lattice pattern or cut out decorative openings to release steam; place on top, making sure to seal the edges.
Brush the top with the beaten egg and sprinkle with a tablespoon or 2 of sugar. Cover the pie with a tent of aluminum foil, being careful not to touch the foil to the pie, so it does not stick. (A trick for this is to fold the foil in quarters before putting it on top. Unfold it and it will form a tent shape.)
Bake at 425° for 30 minutes, then drop the temperature to 375°. Cook for 20 minutes more, then remove the foil. Cook for another 20 minutes with the foil off, or until the filling is thick and bubbly and the crust is golden brown.
This is lovely served either warm or cold.