Prepare pastry and refrigerate. If you are making both pies, do two batches of double-crust pastry. Preheat an oven to 375°.

To make cherry pie, pit cherries with a cherry pitter (remember to do this in a big bowl in the sink or you’ll be splattered with cherry juice). In a large bowl, stir together pitted cherries, cornstarch, sugar, pinch cinnamon or allspice, lemon juice, and almond extract. Be sure to stir until every trace of cornstarch has dissolved.

To make peach pie, bring a large pot of water to boil. Drop in peaches (do in batches if pot is not large enough) and boil for about 30 seconds, then remove with a slotted spoon. When cool enough to handle, slip off skins. Cut peaches into 1/2-inch-thick slices. In a large bowl, stir together peaches, cornstarch, white sugar, brown sugar, pinch salt, and almond extract. Be sure to stir until every trace of cornstarch has dissolved.

Remove pastry from refrigerator and cut in half; rewrap one half with plastic or waxed paper and put back in the fridge. On a lightly floured board, roll the other half into an 11-inch circle. Wrap the pastry around the rolling pin, then unroll it over a 9-inch glass pie pan; snuggle pastry into pan. Pour filling of choice into the pastry, being sure to scrape every last bit of sugary juice from the bowl into the fruit. Trim pastry so it is flush with the rim of the pan.

Remove the other pastry from fridge and roll into an 11-inch circle. With a fluted pastry wheel or a knife, cut into 1-inch wide strips. Arrange strips over pie in a lattice pattern. Or, leave the pastry whole (make decorative cutouts to release steam) and place on top of the pie. Either way, trim the top pastry or lattice strips even with the lower pastry then pinch the edges together to seal. Lightly brush the top with the beaten egg.
   
Bake until the crust is deep golden and the filling is bubbly, 45 to 50 minutes. Remove and let cool completely on a rack. The pies taste great the next day, too.