Preheat the oven to 350°F (standard) or 325°F (convection). Grease and flour two 9-inch cake pans and line with parchment paper.
In a medium bowl, whisk together cake flour, baking powder, baking soda, and salt. Sift & set aside.
Melt chocolate either in a bain-marie (in a bowl over a pot of simmering water) or in the microwave in 30 second intervals. Once melted, allow to cool slightly.
With an electric mixer, or in the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugar together until the mixture is light in color and fluffy.
Add the eggs one at a time, beating well after each addition. Add the vinegar in with the last egg.
Add the melted chocolate and beat until smooth.
Reduce the mixer to low speed, and alternately add the flour mixture and milk. I find that it is best to begin and end with the flour mixture. Scrape down the sides of the bowl as needed. I did this in three additions. Stop mixing as soon as the last of the flour has incorporated.
Portion the cake batter between the two prepared pans and smooth the top with an offset spatula. Bake in the preheated oven for 30-45 minutes. The center of the cake should spring back to the touch, and the edges will look set.
After 5 minutes in the pans, remove to a cooling rack and let cool completely before frosting.
Make the icing & assemble:
Place chocolate and butter in the top of a double boiler over moderate heat and cover until partially melted. Remove from heat and stir until completely melted.
Place all remaining ingredients in a small metal bowl. Beat briefly just until mixed. Fill a larger bowl partially with ice water and nest the small bowl inside. Add the melted chocolate and butter and beat until the mixture thickens slightly. Keeping the small bowl on ice. Stir the chocolate icing with a rubber spatula until the icing thickens.
Spread a light coating on the bottom layer. Align the top layer on the bottom and continue icing the rest of the cake.
Notes
Yield: 8 or 9 inch, 2-layer cakeAdapted from: Maida Haetter’s Book of Great Chocolate Desserts ed. 1981Technique – Be sure to allow the cakes to cool for 5 minutes in their pans before turning out to cool completely, otherwise (even with properly prepared pans) the layers might not come out in one beautiful piece. Also consider popping the cake in the fridge between layers of frosting to get even layers.Variation - Add up to ½ teaspoon of espresso powder to the cake batter or 1 tablespoon to the frosting to amp up the chocolate flavor even more!Storage – Store unfrosted chocolate fudge cake cake well-wrapped at room temperature or in the freezer. Unfrosted cake will keep at room temperature for 3 days, in the fridge for a week or frozen for up to two months! Store unused frosting in airtight containers in the refrigerator for up to 2 weeks. Once frosted, the cake can be kept at room temperature for up to three days.