Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.

In a medium bowl, whisk together the flour, baking soda, cinnamon, nutmeg, and salt. Set aside.

In a large bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Beat in the egg and vanilla extract, then mix in the pumpkin puree until well combined.

Gradually add the dry ingredients to the wet mixture, stirring until just combined.

Fold in the rolled oats until evenly distributed throughout the dough.

In a separate bowl, mix the softened cream cheese, powdered sugar, and vanilla extract until smooth to create the cheesecake filling.

Using a tablespoon, scoop out a portion of the cookie dough and flatten it slightly in your palm. Place a small dollop of the cheesecake filling in the center, then wrap the dough around it to form a ball.

Place the cookie balls on the prepared baking sheet, spacing them about 2 inches apart.

Bake for 12-15 minutes, or until the edges are lightly golden. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.