Preheat oven to 350°F. Grease 3, 8-inch round cake pans. Set aside.
In a medium bowl, add flour, pumpkin pie spice, baking soda, and salt. Whisk together.
In a separate large bowl, cream together softened butter and both sugars until fluffy about 3-4 minutes.
Add in the pumpkin, applesauce, non-dairy milk, oil, apple cider vinegar, and vanilla extract. Mix until combined (ingredients may curdled, which is ok).
Add in the flour in 2 parts mixing after each, being careful not to over mix.
Divide batter evenly into prepared pans. Weigh on scale for accuracy if needed.
Bake for 35-40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Remove pans from oven and let cool. Let them cool completely before frosting.