Preheat oven to 375°F. Line 2 baking pans with parchment paper.
Combine cherries, ¼ cup Torani Amaretto Syrup, cornstarch, and sugar in a small saucepan. Bring to a simmer over medium heat and cook until the mixture is very thick, 1½ minutes. Transfer to a bowl and refrigerate until completely cooled, 15 minutes.
Unroll the pie dough and use a 5-in. round cutter or brûlée dish to cut out 4 rounds from each round of pie dough. Gather up the scraps and reroll them on a lightly floured surface into a 1/8-in. thick round. Cut out 2 more rounds for a total of 10.
In a small bowl, whisk the egg with 1 tbsp. water. Place 1 tablespoon of filling in the center of each round. Brush the edges of each round with egg wash and fold over so the edges meet to create a half-moon. Press the edges together with a fork. Chill the pies for at least 30 minutes.
Brush the pies with the remaining egg wash and poke the tops of each pie once with a fork to vent. Bake until golden brown, 15 to 20 minutes. Transfer the pies to a cooling rack and cool for 30 minutes.
Sift the confectioner's sugar into a medium bowl. Add the remaining 3 Tbsp. Torani Amaretto Syrup, stirring until smooth. Drizzle icing over the hand pies and let stand at room temperature until icing sets.