For the crust: Preheat the oven to 425 degrees F. Cut four 12-inch square pieces of parchment or wax paper.
Mix the flour and salt in a medium bowl. Add the oil and mix with a fork until it begins to come together. Drizzle with the cold water and gently mix. If it looks dry, add additional cold water by the tablespoon. Gather the dough into a ball and divide in half, letting one half be slightly larger than the other (the larger will be your bottom crust).
Place each ball of dough between 2 sheets of the trimmed parchment paper. Use a rolling pin to roll each ball of dough into a circle that almost reaches the edges of the paper, making a 12-inch diameter (the smaller half will be slightly smaller). As you are rolling, continuously rotate the paper so the crust is even.
Flip one of the crusts over and peel off the top piece of paper. Transfer the crust to a 9-inch pie pan paper-side up. Gently peel off the remaining sheet of paper and fit the pastry into the pan, leaving an overhanging edge. Using a pastry brush, brush the inside of the crust with the beaten egg.
For the filling: In a medium saucepan over medium-low heat, combine the cherries, sugar and flour. Bring to a low simmer, stirring often, and cook until the juices release and begin to thicken, 10 to 15 minutes. Transfer the filling to the prepared pie crust. Dot with the butter.
Peel the paper from the remaining crust and flip onto the top of the cherry pie. Use your fingers or a fork to pinch the crusts together to seal. Cut an X vent in the top with a knife. Brush with the beaten egg.
Transfer the pie to a baking sheet and bake for about 20 minutes. Check to see if the edge of the crust is getting dark; if so, use aluminum foil to create a guard around the edge of the pie. Continue to bake until the crust is golden brown, 25 to 35 minutes longer.
Let cool before slicing. Serve with vanilla ice cream.
If using sweet cherries, decrease the sugar by 1/2 cup.