Preheat the oven to 350 F. In a medium bowl, whisk flour, pudding mix, salt, baking soda, and pumpkin pie spice together. In a large bowl, combine butter with pumpkin puree and both sugars until fluffy.
Add in the egg and vanilla extract, and mix until smooth. Add in the flour mixture, mix until it is fully combined. Use a cookie scoop to place the cookies onto a ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.