Prepare the double crust pie pastry. Divide into two disks and refrigerate until needed.
Line a large heavy-duty rimmed baking sheet or pizza stone with foil. Place in the oven and preheat oven to 400°F degrees.
Wash the cherries and drain. Remove the stems and pits.
In a large mixing bowl combine the sugar, almond extract, salt, tapioca, cinnamon, lemon zest and lemon juice.
Fold in the pitted cherries and set aside for 15 minutes, stirring once or twice.
While the cherries rest, roll half the pastry into a circle large enough to fit into a 9-inch deep-dish pie plate with a 1-inch overhang. Gently ease the pastry into the pie pan taking care not to stretch the dough.
Pour the sugar and cherry mixture into the unbaked pie crust. Dot with pieces of butter and refrigerate while rolling out the top crust.
Roll out the remaining disk of pastry and fit over the cherries. Crimp and seal the crust as desired. Cut a few vents for the steam to escape.
Brush the top crust with the beaten egg and milk mixture, then sprinkle with coarse sugar.
Place the pie on the preheated baking pan and bake for 25 minutes at 400°F. Reduce the temperature to 350°F and continue baking for another 35 to 40 minutes or until the crust is golden brown and the filling is bubbling.
Allow the pie to cool to room temperature before serving, about 2 or 3 hours.