Preheat oven to 350˚F and grease 3, 6-inch round cake pans with butter and line them with parchment paper on the bottom. Butter the parchment paper on top and bottom.
Stir the cinnamon, ginger, cardamom, all-spice, nutmeg, and pepper together in a small bowl. Reserve 1 teaspoon of the mixture for the frosting.
In the bowl of a stand mixer beat together the oil, sugar, vanilla, eggs, and Butternut Squash Puree until combined. Add in the flour, baking powder, baking soda, salt, and the spice mixture, minus 1 teaspoon. Stir on low for 1 minute until no flour lumps remain.
Pour the batter into the cake pans spreading it evenly between them.
Bake 30-40 minutes, until the tops are just set, and no longer wiggly in the center. Remove and let cool 10-15 minutes, then run a knife around the edges of the pan and turn the cakes out onto a cooling rack. Cover and let the cakes cool completely before assembling.
If your cakes have domed, trim the tops to make them level and even.