After the pudding mixture has cooled, melt the chocolate in a medium microwave-safe bowl and heat on low for 3 minutes, stirring at 20 second intervals until completely melted. Let sit for 5 minutes to cool.
Add the softened butter to the bowl of your stand mixer fitted with the whisk attachment and whip the butter for about 1 minute, until light and smooth.
Add the pudding mixture in three intervals, mixing on medium and stopping to scrape down the sides and especially the bottom of the bowl to ensure everything is incorporated. Reduce the speed and slowly pour in the cooled chocolate and salt. Increase the speed to high and mix for an additional minute, scraping down the sides and bottom of the bowl. The frosting should look rich and have a dull sheen.
Cut each of the remaining cake rounds in half horizontally with a serrated knife. Place the bottom layer on your cake stand. Place some of the frosting on top and spread evenly just over the edges of the cake. Sprinkle on a layer of cake crumbs and gently press into the frosting. Repeat with the next two layers of cake, frosting, and cake crumbs.
Finally, place the last layer of cake on top, then cover the top and sides of the cake with a very thin layer of frosting and smooth it to make it even. This will be your crumb coating to make it easier for the final layer of frosting. Chill in the refrigerator for 30 minutes to allow the layers and frosting to set. Remove the cake from the refrigerator and coat the top and sides with the remaining frosting and smooth it.
To garnish the cake, hold the cake stand/plate in one hand and with the other, take a handful of crumbs and gently press them into the side of the cake. Continue around the entire side of the cake until evenly covered. Brush off any excess cake crumbs into the bowl below.
Slice and serve immediately.