In a mixing bowl, beat butter and sugar until light and fluffy (about 2 minutes).
Add egg and beat well. Scrape sides and bottom of the bowl.
Add vanilla and pumpkin puree, and mix well.
Lower the speed to low and mix in pudding mix, flour, cinnamon, salt, and baking soda until all combined. Scrape sides and bottom of the bowl, and mix a few more times.
Refrigerate dough for 30 minutes to 1 hour.
Preheat the oven to 350 degrees. Line a large baking sheet with parchment paper.
Scoop cookie dough with a medium cookie scoop (#40 or #50) onto the baking sheet, about 2 inches apart, and bake for 9–11 minutes. (If you have to bake cookies in batches, refrigerate dough in between.)