Preheat the oven to 350 F. Line a 12 cup muffin pan with paper liners. In a medium bowl, whisk together flour, pudding mix, salt, baking soda, and pumpkin pie spice. 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. Evenly divide the cookie dough into the paper liners. Bake for 12-15 minutes.