Preheat the oven to 375°. Spray two 6 inch pans with cooking spray and set aside.
Pour non dairy milk and apple cider into a small bowl and whisk together. Set aside to allow the vinegar to curdle the milk.
Place flour, sugar, cocoa powder, baking powder, baking soda, cinnamon, and salt in a large mixing bowl and stir together. Set aside.
Add applesauce, oil, maple syrup, and vanilla to the milk mixture. Whisk together.
Pour the liquid mixture into the dry mixture and whisk together until completely incorporated.
Divide the batter into the two 6-inch baking pans. Bake for 45 minutes, until a toothpick comes out clean with only a few crumbs.
Allow cakes to cool completely before frosting.