Preheat oven to 400°.
Line baking sheet with parchment paper and spray with cooking spray.
Beat egg in small bowl and set aside.
Mix pumpkin puree, pumpkin spice, vanilla, and brown sugar until smooth.
Place puff pastry on parchment paper or clean surface.
Cut pastry sheet into 9 squares.
Place one tablespoon of pumpkin mix in the middle of each square half.
Brush edges of pastry with beaten egg.
Fold over from corner to corner to form a triangle shape.
Seal edges with fork.
Cut three small incisions into the thickest part of hand puff to allow for steam to release.
Brush tops of puffs with remaining egg wash (there will be a lot off egg wash left over).
Bake for 20 minutes.
While hand pies are baking, mix together powdered sugar and milk.
Once hand pies are golden brown, remove from oven and drizzle glaze on top with a spoon.
Let puffs cool on wire baking rack.