Preheat the oven to 375F. Line a baking sheet with parchment paper.
In a small bowl, mix together the pumpkin puree, sugar, egg and pumpkin pie spice.
Unroll the crescent dough on the baking sheet, separating the triangles. Place about 1 Tablespoon of the pumpkin mixture on each triangle.
Starting with the largest end of the dough, roll the crescent over the pumpkin mix, then slightly pinch the dough closed to keep the filling from leaking out. Continue rolling the dough into a crescent shape.
Bake at 375F for about 10-12 minutes or until golden brown.
For the glaze: Add a small amount of milk to the powdered sugar and stir. Continue adding small amounts of milk and stirring until the icing is a good consistency. If the icing is too thick, add more milk. If it's too thin, add more powdered sugar. Mix until smooth.
Pour the icing into a plastic zip bag.
After the pumpkin pie crescents have cooled for about 10 minutes. Cut off a small corner from the zip bag and drizzle the glaze over the crescents.