Step 1: Make the Cheesecake Filling

1. In a medium bowl, beat together the softened cream cheese, sugar, and vanilla extract until smooth and creamy.
2. Transfer the mixture to a piping bag or a zip-top bag, then place in the freezer for 15-20 minutes to firm up slightly. This will make it easier to work with when stuffing the cookies.

Step 2: Prepare the Pumpkin Chocolate Chip Cookie Dough

1. Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
2. In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy (about 2-3 minutes).
3. Beat in the pumpkin puree, egg, and vanilla extract until well combined.
4. In a separate bowl, whisk together the flour, baking soda, pumpkin pie spice, cinnamon, and salt.
5. Gradually add the dry ingredients to the wet mixture, mixing just until combined. Be careful not to overmix.
6. Fold in the chocolate chips with a spatula until evenly distributed.

Step 3: Assemble the Cookies

1. Using a tablespoon or small cookie scoop, portion out about 2 tablespoons of the pumpkin chocolate chip cookie dough for each cookie and flatten slightly into a disk.
2. Take about 1 teaspoon of the chilled cheesecake filling and place it in the center of the dough.
3. Take another small portion of dough (about 1 tablespoon) and cover the cheesecake filling, sealing the edges by pressing the dough together gently. Roll the cookie into a smooth ball, ensuring the cheesecake filling is completely enclosed.
4. Place the cookie dough balls on the prepared baking sheet, spaced about 2 inches apart, as the cookies will spread slightly during baking.

Step 4: Bake the Cookies

1. Bake the cookies in the preheated oven for 12-14 minutes, or until the edges are lightly golden and the centers are set but still soft.
2. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.