Preheat oven to 350 degrees F.
Line an 8-inch cake pan with a circle of parchment paper cut to fit the bottom of the pan. Set pan aside.
In a large bowl, mix baking soda, sugar, flour, and salt. Dissolve cocoa powder in hot water and then add to dry ingredients. Stir in applesauce, egg substitute, and vanilla. Pour batter into prepared pan. Bake for 35 minutes. Cool cake completely on a cooling rack before frosting with chocolate frosting.
In the bowl of an electric mixer, beat the cream cheese and butter together until smooth. Add sugar substitute and beat until incorporated. Add cocoa powder, salt, and vanilla and beat until blended. If the frosting is too thick to spread, add the milk, 1 tablespoon at a time, with the mixer on low, until spreading consistency is achieved.
Recipe courtesy Juan Carlos Cruz