Preheat oven to 350°F (180°C). Grease a 9x13 inch pan or two 9-inch round pans.
In a small bowl, mix soy milk and apple cider vinegar. Set aside for 5 minutes to curdle and create vegan buttermilk.
In a large bowl, whisk together flour, sugar, cocoa powder, baking powder, baking soda, and salt.
Add the curdled milk mixture, oil, applesauce, and vanilla extract to the dry ingredients. Mix until well combined.
Slowly stir in the boiling water until the batter is smooth. The batter will be thin.
Pour batter into prepared pan(s) and bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Cool completely in the pan before frosting or removing.