1. Preheat your oven to 350°F. Grease and line three 8-inch round baking pans with parchment paper.

2. In a large bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, and pumpkin spice.

3. In a separate bowl, whisk together the dark brown sugar, pumpkin purée, oil, eggs, and vanilla extract until smooth.

4. Add the dry ingredients to the wet ingredients and stir just until combined, being careful not to overmix.

5. Divide the batter evenly among the prepared baking pans. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean. Allow the cakes to cool in the pans for 10 minutes before transferring them to a wire rack to cool completely.

6. In a large bowl, beat the butter and cream cheese together until smooth and creamy. Gradually add the powdered sugar, cinnamon, and vanilla extract, beating until the frosting is light and fluffy.

7. Place the first cake layer on a serving plate and spread the frosting evenly over the top. Repeat with the remaining layers, then frost the top and sides of the cake.

8. Chill the cake slightly before serving to make slicing easier.