Preheat your oven to 350°F. In a medium bowl, whisk together the dry ingredients: flour, baking soda, baking powder, salt, cinnamon, nutmeg, and ginger. Set aside.

In a large bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy. Add the egg and vanilla extract, mixing until well blended. Stir in the pumpkin puree until smooth.

Gradually add the dry ingredients to the wet mixture, mixing until just combined. The dough should be soft and slightly sticky.

In a separate bowl, beat together the cream cheese, powdered sugar, and vanilla extract for the filling until smooth and creamy.

Drop spoonfuls of cookie dough onto a baking sheet, making an indentation in the center of each. Fill the indentation with the cream cheese mixture, then top with more cookie dough to seal the filling inside.

Bake for 12-15 minutes until edges are lightly golden and centers are soft. Let cool on the baking sheet for 5 minutes before transferring to a wire rack.