1. Cut 1/2 cup butter into small cubes; chill butter and almond paste 15 minutes. Stir together flour and salt. Cut butter and almond paste into flour mixture with a pastry blender until it resembles small peas. Gradually stir in vodka and 1/4 cup ice-cold water with a fork, stirring just until dough begins to form a ball and leaves sides of bowl, adding up to 1 Tbsp. more water if necessary. Place dough on plastic wrap; shape into a flat disk.
2. Divide dough into 12 portions. Shape each into a ball. Flatten each into a 3-inch circle on a lightly floured surface; roll into a 5-inch circle. Stack circles between layers of plastic wrap or wax paper. Cover stack with plastic wrap; chill 2 to 24 hours.
3. Preheat oven to 425°. Spread frozen cherries in a lightly greased 13- x 9-inch baking dish; sprinkle with 4 Tbsp. Demerara sugar. Bake 25 minutes or until juice begins to thicken, stirring every 10 minutes. Remove from oven; immediately scrape cherries and juice into a bowl, using a rubber spatula. Stir in dried cherries and next 3 ingredients; cover with plastic wrap. Cool completely (45 minutes).
4. Working with 1 circle at a time, spoon 1 heaping Tbsp. cherry mixture into center of each dough circle; fold dough over filling. Press edges together with a fork to seal. Place on a parchment paper-lined baking sheet.
5. Whisk together egg and 1 Tbsp. water. Brush pies with egg mixture. Cut 1 to 2 slits in top of each pie; sprinkle with remaining Demerara sugar.
6. Bake at 425° for 15 to 20 minutes or until golden. Remove from pan to a wire rack, and cool 15 minutes.