First, prepare your pie crusts and let them chill in the fridge for about an hour. Move the oven rack to the lower third position.
In a small bowl, mix together the sugar, corn starch, and cinnamon.
Pit the cherries and put them in a large bowl. Add the lemon juice and stir. Then, sprinkle the sugar mixture over the cherries and mix until they’re all coated.
Roll out the first pie crust into a 13-inch circle and place it in a 9-inch deep pie pan, letting the edges hang over. Pour the cherry filling into the crust, including any juices. Dot the filling with the diced butter.
Roll out the second crust into a 12-inch circle. Cut it into ten 1-inch strips with a pizza cutter and make a lattice top over the pie. Tuck and crimp the edges. Chill the pie for 30 minutes in the fridge or 15 minutes in the freezer while you preheat the oven to 425°F.
Beat the egg with the milk or water and brush it over the crust. Sprinkle with coarse sugar. Bake the pie on the lower rack for 25 minutes.
Then, place a sheet of foil or a baking sheet under the pie, reduce the oven temperature to 350°F, and bake for another 30-35 minutes, until the crust is golden and the filling is bubbly.