To make the cake:
Position a rack in the center of the oven and preheat the oven to 350 degrees F. Lightly butter the bottom of two 9-inch round cake pans. Line the bottom with parchment paper, then butter and flour the parchment and the sides of the pans.
In the bowl of a stand mixer fitted with the paddle attachment, combine the sugar, flour, cocoa, salt, baking powder, and baking soda, mixing on low speed. Mix in the eggs, oil, and milk.
Increase the speed to medium and beat for 2 minutes. Reduce the speed to low and mix in the water. The batter will be soupy.
Divide the batter evenly between the cake pans. Bake for 30 to 35 minutes, or until a skewer inserted in the center comes out clean.
Remove from the oven and cool on a cooling rack for 5 minutes, then turn the layers out onto the rack and cool completely.
When the cakes have cooled, check the frosting. It should have the consistency of mayonnaise. If it is still too thin, allow it to cool longer.
To make the frosting:
In a small saucepan, combine the sugar and cream and bring to a boil over medium heat, stirring occasionally. Reduce the heat and simmer for 6 minutes. Add the chocolate and butter and stir until melted. Pour into a bowl and stir in the vanilla.
To frost the cake:
Place one cake layer on a serving plate. Spread the frosting with a hot palette knife or icing spatula to give the frosting a beautiful shine. Run the knife under hot tap water and dry with a towel. Spread about 3/4 cup of the frosting over the top of the first layer. Top with the second layer. Spread the remaining frosting over the top and sides of the cake, heating the knife again as necessary.