Preheat your oven to 350°F (175°C).
Grease a 9x13 inch baking pan with butter or cooking spray.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and pumpkin pie spice until well combined.
In another bowl, mix the melted butter, pumpkin puree, and eggs until smooth.
Pour the pumpkin mixture into the dry ingredients and stir until just combined.
Spread the batter evenly in the prepared pan and bake for 25-30 minutes, or until a toothpick comes out clean.
While the cake is baking, prepare the cream cheese topping by beating the softened cream cheese, powdered sugar, and vanilla extract until smooth.
Remove the cake from the oven and allow it to cool slightly before spreading the cream cheese topping evenly over the surface.
Cool completely in the pan before slicing into squares and serving.