Preheat your oven to 350°F & grease your 9" x 13" cake pan *see notes for other pan sizes
Combine the vinegar with the plant milk (soy milk is the only milk that will thicken with vinegar, but you can use another plant milk of your choice)
In a large mixing bowl combine the oil, brown sugar, salt, pumpkin, and then the thickened vinegar/plant milk and with the vanilla & whisk to combine well
Sift the flour with all the spices & the baking soda then add it all at once to the wet mixture in the bowl ~Whisk smooth
Pour batter into your prepares pans & bake immediately in the preheated 350°F oven for 15 minutes
Then turn the oven temperature down to 300°F and bake for the remaining time *see notes above for exact baking times or when a toothpick inserted into the center comes out clean
Cool in the pan(s) until you can touch it without burning your fingers, then turn out onto a cooling rack to cool all the way
Prepare the pumpkin spice buttercream by creaming the vegan butter on high speed with the paddle attachment of your stand mixer (or a hand blender is totally fine!) add the sifted confectioners sugar & pumpkin pie spice 1 cup at a time while blending on low speed until it is all incorporated.
Whip on high speed for 30 seconds to blend well, scrape the bottom & sides of the bowl & continue to mix on low for 3 minutes to smooth
Prepare the ganache icing according to the instructions on that recipe post then let it cool to room temperature to a pourable consistency
Fill & ice the cake with the buttercream then coat with ganache. Orange sugar glaze drizzle is optional
For the Orange Sugar Glaze combine 1 cup of confectioners sugar with 1 tbs plant mil & orange food color whisk smooth then drizzle over the ganache