Preheat the oven to 375° F.

Whisk together the dry ingredients in a large bowl. In a seperate bowl combine the liquid ingredients. Pour the liquid ingredients into the dry ingredients and stir together only until blended.

Line a 12-cup muffin tin with cupcake papers. Fill with batter. Bake until a toothpick inserted into the cupcake comes out clean, about 20 to 25 minutes. Remove cupcakes and place onto a rack to cool.

Whisk together the cocoa powder and sugar in a medium saucepan. Combine the cornstarch or arrowroot and the soymilk together in a bowl, stirring until no lumps remain. Whisk the cornstarch (or arrowroot) mixture into the cocoa-sugar mixture. Start cooking over medium heat, stirring constantly, and scraping the bottom and sides with a rubber spatula until the mixture is glossy - about 7 minutes. Remove from heat and stir in the vanilla. The icing will probably be unavoidable lumpy at this point. The book suggests beating it and straining it through a fine sieve, but I found using an electric egg beater on it worked nicely. Cool completely, stirring occasionally.

When the cupcakes have cooled, spread the icing on them.