In a large mixing bowl stir together the sugar and tapioca. Add cherries and the few drops almond extract; gently toss until cherries are coated. Let stand about 15 minutes or until syrup forms, stirring occasionally.
Meanwhile, in a large mixing bowl stir together all-purpose flour and salt. Using a pastry blender, cut in shortening or lard until pieces are the size of small peas. Sprinkle cold water, 1 tablespoon at a time, over mixture, tossing with a fork after each addition until all is moistened. Divide dough in half. Form each half into a ball.
On a lightly floured surface, use your hands to slightly flatten one ball of dough. Roll dough from center to edges, forming a 12-inch circle. Wrap the pastry around the rolling pin. Unroll onto a 9-inch pie plate. Ease pastry into the pie plate, being careful not to stretch it.
Stir cherry mixture; transfer to the pastry-lined pie plate. Trim the bottom pastry to edge of pie plate. Roll remaining dough as directed above. Cut slits in the top crust. Place top crust on filling. Trim top crust 1/2 inch beyond edge of plate. Fold top crust under bottom pastry. Seal and crimp edge of pastry. To prevent overbrowning, cover edge of pie with foil. Bake in a 375 degree F oven for 25 minutes. Remove foil. Bake for 25 to 35 minutes more or until top is golden and filling is bubbly.
For glaze, in a small mixing bowl combine powdered sugar, cherry brandy or milk, and the 1/4 teaspoon almond extract. If necessary, stir in additional cherry brandy or milk until of drizzling consistency. Drizzle glaze over hot pie. Cool pie on a wire rack. Makes 8 servings.