Small holes cut into the top crust give a sneak preview of the filling.
Preheat oven to 375 degrees. Make the filling: Toss together cherries, sugar, cornstarch, vanilla extract, and almond extract in a bowl.
Make the crust: Roll out 1 disk pate brisee to a 1/8-inch thickness on a lightly floured surface. Fit dough into a 9-inch pie plate. Pour in filling; dot top with butter. Refrigerate while making top crust.
Roll remaining disk pate brisee to a 1/8-inch thickness on a lightly floured surface. Cut out 4 or 5 holes using a 3/4-inch round cookie cutter. Place on top of pie.
Trim bottom and top crusts to a 1-inch overhang using kitchen shears, and press together to seal around edges. Fold edges under; crimp as desired. Freeze for 20 minutes.
Brush crust with egg wash. Bake pie on a parchment-lined baking sheet set on the middle rack, with a foil-lined baking sheet on bottom rack to catch juices, until pie is bubbling in center and crust is golden, about 1 hour 45 minutes. Transfer pie to a wire rack, and let cool before serving.
Pie can be stored at room temperature for up to 2 days.