In a medium bowl, mix together the flour, baking soda, salt and pumpkin pie spice.
In a large bowl, beat the butter until smooth and creamy. Add in the brown sugar, molasses and pumpkin puree until fully combined. Add in the egg and vanilla, and mix in until fully incorporated.
Add in the dry ingredients to the wet ingredients, and mix until fully combined. Cover with cling film, and place in the refrigerator for at least 1 hour.
Preheat the oven to 350˚F. Line two baking sheets with parchment paper, and set aside.
Roll the dough into 1 Tablespoon balls. Roll the balls in the sugar, and place on the prepared baking sheets. Use the bottom of a glass to press down the cookies until they are around 1/2 inch thick.
Place the baking sheets in the preheated oven, and bake for 12-14 minutes. Allow to cool on the baking sheets for 5 minutes, then transfer to wire racks to cool completely.