Cherry pie seems like an all-American dessert, but it’s actually English: Many believe that the first cherry pie was made for Queen Elizabeth I in the late 1500s. English settlers brought pie to America, and the first cherry trees were planted in this country soon after!
Make the crust: Pulse the flour, granulated sugar and salt in a food processor. Add 1 stick cut-up butter and the shortening; pulse until it looks like coarse meal. Add the remaining 1 stick butter; pulse until it is in pea-size pieces. Add the egg yolk and 6 tablespoons ice water and pulse until the dough begins to clump together, adding up to 2 more tablespoons ice water if necessary. Turn out the dough onto a clean surface, divide in half and press into 2 disks. Wrap in plastic wrap and refrigerate until firm, at least 2 hours or overnight.
Meanwhile, make the filling: Combine the cherries, granulated sugar, cornstarch, lemon zest and juice and almond extract in a large bowl. Toss until the sugar is dissolved and the cherries are well coated; set aside.
Roll out one disk of dough into a 12-inch round on a floured surface. Ease into a 9-inch pie plate and trim, leaving a 1-inch overhang. Pour in the filling.
Roll out the other disk of dough into a 12-inch round. Trim the edges, then cut the dough into 3/4-inch-wide strips using a fluted cutter or a knife. (You should have about 12 strips.) Lay half of the strips over the pie, about 3/4 inch apart. Fold back every other strip. Lay another strip of dough perpendicular to the existing strips, then fold the dough back over the new strip. Repeat, folding back every other strip and weaving in new ones, to form a lattice. Trim the strips, leaving a 1-inch overhang. Fold the overhanging dough (strips and bottom crust) under itself, pressing to seal. Crimp the edges with your fingers or a fork, if desired.
Brush the lattice and crust edges with the beaten egg and sprinkle with coarse sugar. Refrigerate the pie until firm, about 30 minutes. Meanwhile, put a baking sheet on the middle rack of the oven and preheat to 400˚ F.
Put the pie on the hot baking sheet and reduce the oven temperature to 375˚ F. Bake until the crust is golden brown and the fruit is bubbling, 55 to 65 minutes. (Tent with foil if the crust is browning too quickly.) Transfer to a rack and let cool completely before slicing.