Place the pumpkin puree in a small saucepan and cook over medium heat for about 10 minutes making sure to stir frequently. Remove and let cool. (The pumpkin should be reduced down to somewhere between 2/3 and 3/4 cup.)
Line a small baking sheet with parchment paper. Set aside.
Cream butter and sugars together in a large mixing bowl. Beat in the cooled pumpkin puree and vanilla until thoroughly combined.
Whisk together flour, cornstarch, baking soda, salt and pumpkin pie spice in a small bowl.
Gradually add flour mixture to wet ingredients, mixing just until combined.
Fold in chocolate chips.
Scoop out about 2 tablespoons of cookie dough and roll into balls. Using a cookie scoop helps to keep the cookies a uniform size.
Place cookie dough balls on the prepared baking sheet and repeat until all dough has been used.
Cover the cookie dough balls with plastic wrap and freeze for at least 30 minutes and up to overnight. If you freeze overnight, let cookie dough balls sit at room temperature for 10 minute before baking. (You can also transfer to a ziploc bag and bake as needed.)
Preheat oven to 350F.
Place cookie dough balls on a parchment lined baking sheet and bake for 10 to 12 minutes. If you would like flatter cookies, press the dough balls down slightly before baking.
Cookies will appear slightly under-baked. Gently press additional chocolate chips into the top of the cookies if desired.
Let cookies cool for several minutes on baking sheet before transferring to a cooling rack.
Store in an airtight container for up to a week.