Preheat the oven to 350°F (180°C) and line a cupcake tray with cupcake liners. Set aside.
Sift the flour and cocoa into a mixing bowl and add the white and brown sugar, baking soda and salt and mix together.
Add the soy milk, vanilla, oil, applesauce and vinegar and mix in. Use a hand whisk to whisk out any big lumps.
Divide the batter evenly between the cupcake liners.
Place into the oven and bake for 20-25 minutes or until a toothpick inserted into the center of one of the cupcakes comes out clean.
Let cool for a few minutes and then remove the cupcakes from the cupcake tray and transfer to a wire cooling rack to cool completely.
Prepare your frosting by adding the vegan butter, powdered sugar, cocoa powder, vanilla and salt to a mixing bowl. Using an electric mixer, start at slow speed, gradually increasing speed. Add in the soy milk slowly, only as much as needed to get the right consistency.
When your cupcakes are cooled, pipe on the frosting and sprinkle with grated vegan chocolate shavings.