Preheat the oven to 350 degrees F and grease an 11 x 17 inch sheet pan.
Measure 1 cup soy milk and add the tablespoon of vinegar to it. Stir slightly and set aside to curdle.
In a large bowl, add the flour, sugar, cocoa powder, baking powder, baking soda and salt. Whisk well to combine.
To the bowl with the dry ingredients, pour in the milk/vinegar mixture, oil, applesauce and vanilla. With a hand mixer (you can skip the mixer and use a large spoon if you need to), mix on medium speed until well combined.
Carefully add the cup of boiling hot water, and mix on low speed until combined. The batter will seem runny, but that is right. It is what makes this cake extra moist and delicious.
Pour the cake batter into the prepared sheet pan, and bake in the oven for 20-25 minutes, until a toothpick inserted in the middle comes out clean. Remove from the oven and make the frosting.
When the cake is done baking, make the frosting: In a medium pot, add the vegan butter, cocoa, soy milk and vanilla. Warm over medium heat, stirring constantly, until the butter has melted and the mixture comes to a simmer. Immediately remove from heat and whisk in the powdered sugar, gradually, until the frosting is smooth.
Pour the warm frosting over the still warm cake, spreading evenly with a spatula or spoon. Sprinkle with optional nuts, if using.
Let the cake and frosting cool for at least 30 minutes if possible before slicing and serving. Enjoy!