Thaw pastry rounds on parchment lined sheet tray. Place a scant 2/3 cup of butterscotch pudding on half of round. Brush edges of pastry with beaten egg, then gently fold over and crimp edges. If desired, brush tops with additional beaten egg and sprinkle with granulated sugar. Make vents in the top with a sharp knife.
Bake until pastry is golden brown, approximately 20-23 minutes. Cool until room temperature.
Whisk together powdered sugar, cocoa powder, and milk until a drizzle consistency. Drizzle gently over hand pies. Let set for 10 minutes and serve.