Preheat oven to 350°F. Grease a 15” x 10” x 1” jelly roll pan with butter; set aside.
In the bowl of an electric mixer, fitted with the whisk attachment, beat together the pumpkin, butter, oil, vanilla, and sugar. Add in the eggs and mix to combine. Add in the dry ingredients, and beat until just combined.
Pour the batter into the prepared pan, and spread evenly.
Bake for 20-30 minutes, until a toothpick inserted into the center comes out clean. Allow to fully cool.
For the Frosting:
In a food processor, process together the sugar and lavender, until the lavender is ground, and the sugar is fragrant.
Add the lavender sugar, and the rest of the ingredients to the bowl on an electric mixer fitted with the paddle attachment. Beat for 5-8 minutes until light and fluffy.
Spread the frosting over the cooled cake, slice, and enjoy!