To Make the Pumpkin Spice Cake:
Preheat the oven to 350 degrees F. Grease the medium pan from the Falcon Bake Set with cooking spray.
In a medium bowl, whisk together the flour, sugar, baking powder, pumpkin spice, baking soda and salt.
In a separate bowl, whisk together the eggs, neutral oil, pumpkin puree and vanilla extract until smooth.
Add the dry ingredients and mix until just combined. Pour the pumpkin spice batter into the pan and smooth it out using an offset spatula or butter knife. Transfer to the oven to bake for 25 to 30 minutes, or until a skewer comes out clean. Allow to cool.
To Make the Brown Butter Frosting:
Add 1/2 cup of the butter to a small saucepan. Set over medium heat. Let melt and come to a bubble. Cook, stirring occasionally, until little brown specks form and it smells nutty. Remove from heat and allow to cool to room temperature. You can put it in the freezer for 10-15 minutes for faster cooling.
Add browned butter and the last 1/4 cup softened butter to a stand mixer with the whisk attachment. Sift in the powdered sugar and add the vanilla extract, salt and heavy cream.
Beat the frosting for about 3 minutes. Add more powdered sugar if too loose and more cream if too stiff.
To Assemble the Cake:
Pour the frosting on the cooled sheet cake and spread! If choosing to frost the little pumpkins on the top, reserve a cup of the frosting to tint with food coloring and pipe on top using a squeeze bottle.
Then, cut your pumpkin spice cake into slices and enjoy!