Place oven rack in center position and heat oven to 350 degrees F. Generously butter or grease two 9-inch round cake pans, or a 9-by-13-inch baking pan; dust pans with cocoa powder, knocking out excess; set aside.

Blend chocolate into hot water until melted; set aside to cool. In a large bowl, cream together butter and brown and white sugars with an electric mixer on high speed until light and fluffy. Add eggs, one at a time, beating after each addition. Carefully beat in melted chocolate, scraping down the sides of bowl with a spatula as needed. In a medium-sized bowl, whisk together flour, baking soda, and salt. Add dry ingredients alternately with the buttermilk to the chocolate mixture and beat on low to medium, scraping down the sides of bowl with a spatula as needed, until evenly combined and batter is smooth and glossy. Beat in vanilla. Pour batter into prepared pans and spread evenly.

Bake 9-inch rounds for 30 to 35 minutes, or 9-by-13-inch pan for 35 to 40 minutes, or until a toothpick or cake tester comes out clean and sides are slightly pulling away from edge of pans. When done, remove from oven and let cool in pans on wire rack for 10 minutes. Remove from pans onto a wire rack and let cool completely before frosting.

Chocolate Frosting

Combine sugar, salt and milk in large heavy saucepan. Heat on low, stirring until sugar melts. Raise heat to medium and bring to a boil, stirring constantly. Reduce heat to low; simmer 6 minutes without stirring. Remove from heat. Add chocolate; stirring until chocolate is completely melted. Stir in butter and vanilla, until melted and well combined. Chill until mixture begins to thicken (or if you're short on time, place the bowl over an ice bath). Beat until thick and creamy enough to spread. Makes enough to fill and frost one 2-layer 8- or 9-inch cake. (If making a 9-by-13-inch cake, cut the frosting recipe in half.)

Frost Cake

Before frosting cake, place 4 strips of waxed paper around edge of a cake plate (waxed paper will protect plate as you frost), and brush loose crumbs from sides and edges of cooled layers. Place one layer, rounded side down, on prepared cake plate, spread about 1/2 cup of frosting to within 1/4- inch of edge. Place second layer, rounded side up, on frosted layer. Coat side with very thin layer of frosting to seal in crumbs. Swirl more frosting on side, forming a 1/4-inch ridge above top of cake. Spread remaining frosting over top of cake, just meeting the built-up ridge around side. Make attractive swirls or leave the top smooth for decorations. Remove waxed paper pieces by easing them gently to the left and then the right. Slide each one out the side; don't pull them out. Remove each piece by sliding in the same direction.

To slice cake, do so with a thin, sharp blade. Cut straight down to the bottom. When slice is free, slide it out; do not lift it through the cut otherwise it will take cake and frosting with it.