FROSTING. Chop both chocolates into coarse bits and melt in a double boiler set over hot (not boiling) water; stir occasionally until completely melted.
Remove pan from hot water and allow the chocolate to cool until just no longer warm to the touch, about 20 minutes.
Place the butter in a bowl and beat in the cooled chocolate until the mixture is evenly blended, about 3 minutes - Frosting can be stored at a cool temperature for up to 3 days, or several months in the freezer.
Heat the oven to 350; butter two 9-inch round cake pans and line them with buttered and floured parchment paper or waxed paper.
FUDGE CAKE. Sift the flour; measure 3 cups.
In a large bowl, mix together the flour, sugar, baking powder, baking soda and salt, breaking up any lumps of sugar.
In a small bowl, whisk about 1/2 cup of the milk with the eggs and vanilla; set aside.
Chop the chocolate into coarse bits and melt in a double boiler set over hot (not boiling) water.
Combine the remaining cup of milk and the butter with the mixed dry ingredients and beat for 1 1/2 minutes, scraping the sides of the bowl twice; add the egg mixture in 3 parts, scraping the sides of the bowl and beating for 20 seconds after each addition.
Add the melted chocolate and beat until just incorporated.
Pour the batter into the prepared pans and bake in the center of the preheated oven until the cake springs back when lightly pressed in the center, 25 to 30 minutes.
Cool the cakes in their pans for 10 minutes and invert onto racks; cool completely before frosting.
Frost the top surface of one layer of cake and top with the second layer; spread the remaining frosting on the top and sides of the cake.
Make a decorative pattern zigzag in the frosting by pulling a serrated knife across the surface in a back-and-forth motion.
Use a small spatula or spoon handle to pull out spikes of frosting all around the sides; cake can be completed a day ahead and refrigerated.
SERVING: Return to room temperature if refrigerated; cut into wedges and serve.