Preheat the oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a medium bowl, whisk together the flour, baking soda, pumpkin pie spice, cinnamon, and salt.

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

Add the egg, vanilla extract, and pumpkin puree to the butter mixture and mix until smooth.

Gradually stir the dry ingredients into the wet ingredients until just combined. Fold in the white chocolate chips, if using.

In a separate small bowl, beat the cream cheese, powdered sugar, and vanilla extract until smooth.

Scoop the cookie dough onto the prepared baking sheets, leaving space between each cookie. Add a small dollop of the cream cheese mixture to the center of each cookie and gently swirl or press it in slightly.

Bake for 11 to 13 minutes, or until the edges are set and the centers look slightly soft.

Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.