Using the paddle attachment on a stand mixer, a food processor, or a pastry cutter, incorporate the butter into the flour and salt until it is broken into pea-sized pieces.
Add the ice water and mix until the dough just begins to come together.
Turn onto a clean counter and knead lightly one or two times to form a solid ball.
Divide the dough into two even pieces, form each into a disc, and wrap in plastic wrap. Refrigerate for at least one hour, or up to 3 days.
Once the dough is chilled, roll it out until it will fit the base of a pie plate, with a little bit of excess.
Roll the dough carefully onto the rolling pin and transfer it to the plate. Press into the bottom of the pie dish, then trim around the edges of the plate. Place back into the refrigerator for at least half an hour to chill.
For the Filling:
Combine the cherries, vinegar, sugar, and salt in a bowl and let macerate for an hour.
Once the sugar has dissolved and the cherries have formed a puddle of liquid in the bottom of the bowl, transfer them to a medium-sized saucepot and cook on medium-low heat for fifteen minutes, stirring regularly.
After the filling has thickened, turn off the heat and stir in the arrowroot until it has dissolved.
Let the filling cool slightly while you roll out the second half of the pie dough. If desired, cut a design into this top piece. Preheat the oven to 375°F.
Transfer filling to the chilled shell. Roll the second half of the dough over the top.
Trim the top so that it is the same size as the edge of the bottom of the shell. If you did not cut a design in the top crust already, use a knife to slice 4 1-inch vents in the top dough. Using a fork, crimp the edges of the crust together.
Whisk the egg with 1 tablespoon of water. Using a pastry brush, brush this egg wash over the top of the pie.
Bake for 30 minutes, until the top is slightly browned.