In a large mixing bowl add the pumpkin puree, sugars, oil, eggs, and vanilla extract. Whisk until fully combined. Make sure to scrape down the sides of the bowl to ensure everything is evenly combined.
Place a fine mesh sieve over the wet ingredients and sift in the flour, baking soda, baking powder, salt, and pumpkin pie spice. Using a rubber spatula and gently fold into wet ingredients
In a small saucepan brown the butter, once browned pour into a heat-proof bowl to cool for 5 minutes. Add the confectioner's sugar, vanilla bean paste, and cream and whisk to combine.
Pour on top of the cooled pumpkin cake, and use an angled spatula to gently spread the frosting into an even layer. Let the frosting set for 30 minutes.