Combine the chocolate, sugars, butter, and water in a medium saucepan and place it over medium heat. Cook, stirring, until the mixture is melted and smooth. Remove the pot from the heat and let it cool while you prepare the remaining ingredients.

Combine the flour, baking soda, baking powder, and salt in a bowl; whisk to blend the ingredients.

Whisk the milk and eggs together in a mixing bowl. Add the slightly cooled chocolate mixture, whisking to blend thoroughly. Add the dry mixture, a little at a time, whisking each addition until smooth.

Pour the batter into the prepared fluted cake pan.

Bake the cake for 33 to 38 minutes, or until a skewer inserted into the center of the cake comes out with only a few crumbs clinging.

Let the cake cool in the pan on a rack for 10 minutes.

Carefully invert the cake onto a plate.

For the frosting, combine the butter and chocolate in a saucepan and place it over medium-low heat. Cook, stirring constantly, until the mixture is melted and smooth. Remove the pan from the heat and add the salt, confectioners' sugar, vanilla, and 2 tablespoons of boiling water. Whisk until smooth and well blended. Continue adding boiling water, 1 to 2 teaspoons at a time, until the desired consistency is reached.

Spoon the glaze over the cake, letting some of it drip down the sides.