Make the cake:
Position a rack in the center of the oven and heat the oven to 325°F. Lightly grease a 9x2-inch round cake pan, line the bottom with parchment, and flour the sides (but not the bottom).
Sift the cake flour, cocoa powder, baking powder, baking soda, and salt into a large bowl. Add the sugar and whisk until well blended. Measure the oil into a 1-cup liquid measure, add the egg and vanilla, and mix with a fork to blend. Add the egg-oil mixture to the dry ingredients and then add the water. Whisk until the dry ingredients are just moist, about 1 minute, scraping down the sides of the bowl. Pour the batter into the prepared pan.
Bake until a pick inserted into the center of the cake comes out clean, 32 to 34 minutes. Let cool on a rack for 20 minutes. Lightly grease a wire rack, invert the cake onto it, lift off the pan, peel off the paper, and let the cake cool completely.
Make the mousse:
Set up an ice bath by partially filling a large bowl with cold water and some ice.
Combine the cream and cocoa in a large saucepan set over medium heat. Bring to a full boil, whisking occasionally to blend in the cocoa. Slide the pan off the heat and immediately add the chopped chocolate and the butter; whisk slowly until melted and smooth.
Scrape the chocolate mixture into a large bowl. Add the vanilla and salt. Set over the ice bath and stir constantly with a rubber spatula, scraping the sides very frequently, until the chocolate cools to room temperature (don’t stop stirring or lumps will form) Remove the bowl from the ice bath.
Put the whites in a large clean bowl. Whip with an electric mixer on medium-low speed until very foamy. Increase the speed to medium high and beat until the whites form very loose, soft peaks. Slowly add the sugar. Continue beating until the whites are shiny and form floppy peaks.
Working quickly, scoop about a third of the whites into the cooled chocolate mixture and fold together with a rubber spatula or a whisk until blended. Scrape the remaining whites into the chocolate and fold together gently but thoroughly. Scoop out about 1 cup of the mousse into a bowl, cover, and refrigerate for finishing touchups. Use the rest of the mousse to assemble the cake.
To assemble the cake:
Set the ring of a 9-inch springform pan on a large, flat cake plate. To cut the cake into layers, it helps if the cake is slightly chilled. Set the cake bottom side up on a parchment-lined work surface. Cut into three equal layers. Set aside without separating the layers.
Gently flip the top cake layer (really the bottom) upside down and center it in the springform ring so the mousse can flow over the edge to frost the sides; handle the cake carefully (if it breaks, just piece it together). Scoop about one-third of the mousse (a heaping 2 cups) onto the cake layer in the ring and gently spread to cover. Flip the next cake layer (the center) on top of the mousse and press gently to level it, if necessary. Scoop half of the remaining mousse over the layer and spread gently. Flip the remaining cake layer upside down and set it on top of the mousse. Press gently to level it. Spread on the remaining mousse and smooth the top; the cake should fill the ring (don’t worry if a little mousse leaks out of the bottom).
If you’re decorating the cake with nuts, add enough mousse to the top layer of the cake so it comes to the rim of the springform ring. Smooth the top with a metal spatula or the flat, straight edge of a long knife. Pull an icing comb or a long serrated knife across the mousse, making a wavy pattern. If the pattern doesn't hold, pop the cake in the fridge for 5- to 10-minute intervals so the mousse starts to set, and then try again. (If you're wrapping the cake with a chocolate band, skip this step) Put the cake in the fridge for at least 6 hours and up to 24.
Take the cake from the fridge. Run a long, thin knife or metal spatula under hot water and dry it well. Slide the warm knife between the cake and the ring, pressing the knife against the ring, to loosen the cake. Carefully release the springform clasp; gently pry it all the way open. Lift off the ring and clean the plate edge. If you’re decorating the cake with nuts, mold strips of foil around the cake plate to keep it clean.
If the cake’s sides have bare patches, use a small metal spatula to touch them up with some of the reserved mousse. Chill the cake.
To decorate with nuts: Scoop up a handful of the walnuts in one hand and pat them onto the side of the cake. Many will fall off but you'll be left with a single layer of nuts. Repeat, rotating the cake to cover all the sides.
To decorate with a chocolate band, follow the method demonstrated in the video.
Once decorated, keep the cake refrigerated and serve it within 8 hours. Remove from the fridge 10 to 15 minutes before serving.
Photo: Scott Phillips