In a large bowl, beat the cream cheese, sugar, and cornstarch until smooth.
Add pumpkin puree, sour cream, vanilla, and pumpkin pie spice. Mix until combined.
Beat in the eggs one at a time until just combined.
Pour the batter over the cooled crust and bake for 42-45 minutes until the center is slightly jiggly.
Let the cheesecake cool completely, then chill in the fridge for at least 6 hours.