Preheat oven to 325°F // 160°C // Gas mark 3. Prepare an 8x8 inch square cake pan by lining with 2 pieces of overlapping parchment and wrapping pan in cake strips, if desired. Secure parchment and cake strips with clips.

In a medium mixing bowl, whisk together the flour, cornstarch, baking powder, baking soda, cinnamon, pumpkin pie spice and salt. Set aside.

In a large mixing bowl, beat butter with both sugars until light and fluffy.

Add eggs, one at a time, beating until fully incorporated, then add vanilla and beat until combined.

Lastly, add oil and pumpkin purée and beat until smooth.

Add dry ingredients to butter mixture and beat until smooth.

Pour cake batter into prepared pan and bake for 25 - 35 minutes. Check cake at 25 minutes, then every few minutes thereafter. Baking time will depend on your oven. Remove cake when a tester comes out with a few moist crumbs attached.

Let cake cool in pan for 5 minutes before removing from pan and placing on a cooling rack to cool completely.

While cake is cooling, make frosting: Cream butter and cream cheese together with an electric hand mixer until fluffy, about 4 minutes. Add vanilla and a pinch of salt, mix to combine.

Add powdered sugar in 2 batches, thoroughly mixing between additions and whipping for 30 seconds after second addition to make it light and fluffy.

Spread frosting over the cake and smooth top with an offset spatula. Top with sprinkles if desired.