Whisk together the cream cheese, sugar and vanilla extract until smooth and combined. Place 9 teaspoons (use half teaspoon if you'd like a thinner layer of cheesecake) of the mixture on a baking tray lined with parchment paper. Freeze until solid - about 1 - 2 hours.
For the Cookies
Preheat the oven to 180C/350F/Gas 4, and line a baking tray with parchment paper or a silicone mat. Set aside.
Whisk together the flour, baking soda, cornflour, salt, and spices. Set aside.
Whisk together the butter and sugar until combined. Add the pumpkin puree and vanilla, and mix until combined. Add the dry ingredients, and mix until combined.
Roll the dough into 2oz balls, about 9 big balls. Form the balls into flat circles, and place 1 teaspoon of the frozen cheesecake mixture into the centres. Form the dough back into balls, sealing the cheesecake inside.
Place the dough balls on the prepared baking tray, and bake for 12 - 14 minutes. Allow to cool on the baking tray for 5 minutes before transferring to a wire rack to cool completely.
Notes
If desired, you can make smaller cookies. Make sure to use less cheesecake mixture per cookie.Cookies stay fresh in an airtight container at room temperature for up to 1 week.Cookie dough balls can be kept in the fridge for up to 5 days, or frozen for up to 3 months. Bake from frozen for an extra minute.