Preheat the oven to 350 degrees F. Butter and lightly flour two 9-inch round cake pans.

Cream the butter in a standing electric mixer fitted with the paddle attachment. Add the brown sugar and eggs and beat until mixture is light and fluffy, 2 to 3 minutes.  Add the vanilla and melted chocolate and mix to blend. Add the baking soda and salt and mix briefly. Sift the flour onto a piece of parchment paper. Sift the cocoa powder next to it on the same piece of parchment. Spoon all of the cocoa powder into a measuring cup, then spoon enough of the sifted flour into the measuring cup until you have 2 ¼ cups of flour and cocoa combined. (Discard any remaining flour or save for another purpose.) Add the flour mixture in three batches, alternating with the sour cream, and beating just until smooth. Combine the boiling water and espresso powder and add to the batter, mixing just until incorporated. Divide the batter evenly between the two pans. Bake in the center of the oven until a tester inserted in the center of the cakes comes out clean and cakes just begin to pull away from the sides of the pans, usually 25 to 30 minutes. Cool the cakes in the pans on a wire rack for 10 minutes, then turn out onto racks and cool to room temperature.

When the cakes have cooled and you are ready to assemble the cake, cut any pronounced doming off of the top of the layers (save to make crumbs for coating outside of cake if desired -- see note below). Using a long, serrated knife, cut each layer into two even pieces horizontally.

Place one layer onto a cake plate and top with 1/3 of the pudding, spreading to form an even layer of pudding. Top with a second cake layer and another 1/3 of the pudding. Repeat with the third layer and the remaining pudding. Top the cake with the final fourth cake layer. Using some of the frosting, coat the cake with a thin crumb coating and then refrigerate cake briefly until the frosting has firmed up. This will lock in any loose crumbs and thus make frosting the cake easier. Continue adding layers of the frosting until you have a smooth, even layer on all sides and a nice, even coating on top.  If desired, coat sides or top of cake with fine cake crumbs. Refrigerate cake briefly or up to overnight before serving. (Return to cool room temperature before serving.)

Note:  Regarding making cake crumbs -- this is a very moist cake, so crumbling can be tricky. If you want to add crumbs to the outside of your cake and you are having trouble crumbling, you can place the cake pieces in a low (275 degree F) oven for 5 to 10 minutes, and then allow to cool completely. Place cooled pieces in a medium sieve and rub cake pieces around, pressing against the sieve and collecting the crumbs in a bowl. Press crumbs onto outside of cake as desired,