Prepare: Preheat the oven to 350 degrees F and line a 12-cup muffin pan with paper liners.
Make Vegan Buttermilk: In a glass measuring cup, combine the unsweetened soy milk and apple cider vinegar. Let it sit for a few minutes to curdle (this is your vegan buttermilk).
Mix Dry Ingredients: In a large bowl, whisk together the flour, cocoa, sugar, baking powder, baking soda, and salt until combined.
Add Wet Ingredients and Mix Batter: To the bowl with the dry ingredients, add the vegetable oil, applesauce, vanilla, and vegan buttermilk. Stir with a large spoon until well-combined, but do not over mix.
Bake Cupcakes: Fill the liners about 3/4 of the way full. Bake for 20-24 minutes, or until a toothpick comes out clean with no wet batter. Avoid opening the oven as they bake, or they may deflate.
Cool: Remove from the oven and let cool in the pan for 10 minutes, then transfer to a cooling rack and let the cupcakes cool completely before frosting.
Make Chocolate Frosting: Using an electric mixer (hand or stand mixer), beat the vegan butter until smooth and creamy, about 1-2 minutes. Sift in the cocoa powder and 2 cups of the powdered sugar, if clumpy. Add the vanilla and 2 tablespoons of milk, and start mixing on low speed, then increasing to high and beat for 2-3 minutes, until fluffy. Add more powdered sugar if it seems too runny, or a little more milk if it's too thick.
Decorate and Serve: Use a piping bag and tip to pipe frosting onto the cooled cupcakes, or simply spread frosting on thick using a butter knife. Serve and enjoy!