Preheat the oven to 400°F. Place a large rimmed baking sheet in the oven to preheat.
Open the cans of cherries and drain them, reserving the juice from one can. You'll need ½ cup of liquid.
Pour the liquid, sugar, cornstarch, lemon juice, and salt into a 2-quart saucepan and set over medium heat. Whisk constantly over the heat until the mixture is boiling and has thickened. This will take a few minutes, so be patient. You'll know the mixture is thickening when globs suddenly appear in the mixture.
Remove from the heat and whisk in the almond extract and butter until smooth and well blended. Gently fold in the drained cherries with a flexible spatula, then set aside to cool.
Roll the chilled pastry on a lightly floured surface until it's about ⅛-inch thick. Use it to line a 9-inch metal pie plate, then trim off the excess pastry with a knife. Gently spread the cooled cherry filling in the pastry.
Wad up the remaining pastry and re-roll it to about ⅛-inch thick. Cut into strips, using a ruler for straight lines. Lay several of the strips horizontally across the top, then weave the remaining strips under and over the other ones to create a lattice top. Cut off the excess pastry, crimp the crust, and brush the pastry with beaten egg. Sprinkle liberally with demerara sugar if desired.
Bake at 400°F for 20 minutes, then reduce the heat to 375°F and bake for another 20 minutes. The crust should brown beautifully and the filling should bubble gently.
Remove the pie from the oven and let it cool for 3-4 hours on a wire cooling rack to allow the filling to cool and set. Cutting it too soon will make the filling runny.
Serve with vanilla ice cream.