Preheat oven to 350 degrees and spray a 9x13-inch baking pan with baking spray with flour.
Place the chopped chocolate in a medium bowl. Pour the boiling water over it. Let stand until chocolate is completely melted, stirring a few times. Let cool to tepid.
Sift the flour, baking soda, and salt onto a piece of waxed paper.
Using an electric stand mixer, beat butter and shortening on medium speed for 3 minutes.
Add the superfine sugar in three additions, beating for 1 minute after each addition.
Beat in the eggs one at a time, beating for 45 seconds after each addition. Scrape down the sides of the bowl several times.
Slowly beat in melted chocolate and vanilla.
On low speed, beat in the flour mixture in 3 additions, alternating with the buttermilk in 2 additions. Scrape down the sides of the bowl several times during these additions.
Transfer the batter to the prepared baking dish, smoothing it out.Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean.
Cool the cake before frosting.
To make frosting, place half of the confectioners' sugar and the salt in the bowl of an electric mixer.
In a separate bowl, whisk together the melted chocolate and butter until blended.Transfer to the bowl with the confectioners' sugar. Beat for 1 minute on LOW speed.
Add the milk and vanilla and beat for 2 minutes on medium speed. Scrape down the sides of the bowl.
Add the remaining confectioners' sugar and mix in.
Add the heavy cream and beat on medium-high speed for 2 minutes. Add a little more heavy cream if too thick.
Spread frosting on cake.