Preheat the oven to 400º F and line a baking sheet with parchment or a silicone baking mat.
Roll the pastry sheet out onto a cutting board or flat surface. Using a large biscuit cutter or the rim of a drinking glass cut 4" round circles in the dough (save the scraps to roll out again and cut more circles).
Place the dough circles onto the prepared baking sheet.
In a medium-sized bowl mix the pumpkin puree, shredded cheddar cheese, diced onion, cumin, paprika, and egg together until smooth.
Scoop about 1 tablespoon of the pumpkin mixture into the center of each dough circle leaving the edges clear.
Fold the circle over so it makes a half-circle and use the prongs of a fork to crimp and press the edges together. Repeat this process with all the dough circles.
In a small bowl, whisk the egg and milk together. Using a pastry brush coat the top of each pastry with the egg wash.
Using a sharp-tipped knife cut 3 small slits (or a lightening bold shape) into the top of each pastry.
Sprinkle coarse salt on top of each pastry and bake for 15 minutes. Rotate the pan and bake for another 5 to 10 minutes until the tops become golden brown.
Allow the pastries to cool slightly before eating.