Preheat the oven to 350 degrees F and grease two 8-inch round cake pans. Place a round of parchment paper on the bottom for easy removal.
In a large bowl, whisk the pumpkin puree, oil, milk, sugars and vanilla until smooth and well combined.
Now add the flour on top of the wet ingredients. Sprinkle the baking powder, baking soda, salt, cinnamon and pumpkin pie spice on top of the flour and whisk or stir until just combined.
Pour evenly into the prepared pans and bake for 35-45 minutes, until a toothpick inserted in the middle comes out clean.
Let the cakes cool in the pans for 10 minutes, then carefully invert on to a cooling rack and let cool completely before frosting. If desired, slice the dome off each cake layer before frosting.
Make the frosting - In the bowl of a stand mixer with paddle attachment (or using a handheld mixer), beat the butter until smooth. Now add the powdered sugar gradually, until it's mixed in. Add the espresso powder, vanilla and 2-3 tablespoons plant milk, as needed. Beat on medium-high speed until fluffy, smooth and well combined.
Once the cake layers are completely cooled, frost, serve and enjoy!