To prepare the cake, preheat the oven to 350°. Lightly grease the bottoms and sides of 2 (9-inch) round cake pans with butter; line the bottoms with wax paper. Coat the wax paper with butter. Break 4 ounces of chocolate into pieces, and place them in a microwave-safe bowl. Microwave on high for 1 minute. Stir; microwave on high 30 seconds. Stir until the chocolate melts. Cool.
Whisk 2/3 cup boiling water and cocoa together in a medium bowl; stir in milk and 2 teaspoons vanilla. Set aside. Place brown sugar and 8 tablespoons butter in a large bowl; beat with a mixer at medium speed 3 minutes, or until well-blended. Add the eggs, 1 at a time, beating well after each addition; stir in the melted chocolate. Lightly spoon the flour into a dry measuring cup, and level with a knife. Combine the flour, baking soda, and 1/4 teaspoon salt, stirring well with a whisk. Add the flour mixture and cocoa mixture alternately to the egg mixture, beginning and ending with the flour mixture. Blend well after each addition. Pour the batter into the prepared pans. Bake at 350° for 30 minutes, or until a wooden pick inserted into the center comes out clean. Cool in pans 10 minutes on wire racks; remove from pans. Cool completely on wire racks.
To prepare the frosting, combine the cream and granulated sugar in a medium saucepan over medium heat. Cook until the sugar melts, stirring frequently. Cook an additional 5 minutes, stirring constantly (do not boil). Place the chopped chocolate in a large mixing bowl, and pour the cream mixture over the chocolate. Stir until chocolate melts. Add 6 tablespoons butter, and stir until it melts. Stir in 2 teaspoons vanilla and 1/4 teaspoon salt. Refrigerate 30 minutes, or just until cool. Beat with a stand mixer using the whip attachment (or hand mixer) at high speed until the mixture thickens to a light, spreadable consistency (about 12 minutes).
Place 1 cake layer on a plate or cake stand. Spread with about 1 cup frosting. Top with the second layer. Spread remaining frosting over sides and top of cake.