Make the Frosting first. Put the chopped chocolate in a medium bowl. Bring the cream to a boil in a 2-quart saucepan over medium-high heat. Pour the hot cream directly over the chocolate and let it sit without stirring for 5 minutes. Using a whisk, stir in the center of the mixture in a small, tight circular motion until fully combined. Add the butter and stir until it is fully incorporated. Put a piece of plastic wrap directly onto the surface of the chocolate mixture and set aside at room temperature for at least 8 hours or overnight.
Make the Cake.
Position a rack in the center of the oven and heat the oven to 350 degrees. Butter two 8 x 2-inch round cake pans and line each with a parchment paper round. Butter the parchment paper and dust with flour. Tap out any excess.
With a mixer, beat the butter, brown sugar, and vanilla on medium-high speed until lighter in color and slightly increased in volume, 3 to 5 minutes. Lower the speed to medium and add the eggs, one at a time, mixing until each is fully incorporated before adding the next. Sift the flour, cocoa powder, baking soda, and baking powder onto a piece of parchment paper. Add the salt to the dry ingredients after sifting. Using the parchment as a chute, add one-quarter of the dry ingredients to the batter and mix on low speed until incorporated. Add about 1/2 cup of the buttermilk and mix on low speed until incorporated. Continue to alternate dry ingredients and buttermilk, mixing until incorporated after each addition and stopping to scrape the bowl and beater as necessary. Using a whisk, fold the mayonnaise into the batter.
Divide the batter evenly between the prepared pans and bake until a toothpick inserted in the center of the cakes comes out clean and the sides of the cake have begun to pull away from the pan slightly, 40 to 45 minutes. Remove the pans from the oven and cool on a rack for 15 minutes. Invert the cakes onto the rack and remove the pans and parchment. Cool the cakes completely.
With a serrated knife, cut each cake in half horizontally. Put one of the base layers on a cake plate and tuck strips of waxed paper under the cake to keep the plate clean while icing the cake.
Top the cake with about 1/3 cup of the chocolate frosting, spreading it evenly over the top. Add another cake layer, top with frosting, and repeat until the last layer is in place.
Spread a thin layer of frosting over the top and sides of the cake and refrigerate for 15 minutes to seal in any crumbs. Spread the remaining frosting over the top and sides. Remove the waxed paper. I patted some shaved chocolate curls all around the sides of the cake for garnish.