Preheat your oven to 350°F (175°C). Cream together butter, brown sugar, and granulated sugar until pale and fluffy. Add pumpkin purée, egg, and vanilla, mixing thoroughly.

In a separate bowl, whisk together flour, baking soda, baking powder, salt, pumpkin pie spice, and cinnamon. Gradually fold into wet ingredients until a dense dough forms.

Cover dough with plastic wrap and refrigerate for at least 1 hour.

Beat together cream cheese, additional sugar, vanilla, and flour until smooth. Cover and chill the filling.

Scoop tablespoon-sized portions of dough, roll into balls, and flatten slightly on a baking sheet. Bake for 10-12 minutes.

After cooling, fill each cookie's center with cheesecake filling.

Chill cookies for 30 minutes before serving.