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1
Make the cake: Grease three 8-inch round cake pans, and line the bottoms with parchment paper. Preheat the oven to 350u00b0F (175u00b0C).
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2
Place the chicory in a heatproof bowl. Pour the boiling water over the chicory and let it steep for 10 minutes. Strain the brewed chicory through a fine-mesh sieve and measure 1 cup (240ml) into a large measuring cup. Discard the solids. Whisk the brown sugar and mayonnaise into the brewed chicory until no sugar lumps remain (if it looks curdled, that's fine) and set aside.
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3
In a large bowl, whisk together the flour, cocoa, baking soda and baking powder. Add the chicory liquid and vanilla to the dry ingredients and whisk until smooth. Divide the batter among the three prepared pans and smooth their tops. Bake for 20 minutes or until the tops spring back when lightly pressed. Let the cakes cool in their pans for 15 minutes, then invert onto cooling racks; remove the pans, carefully peel away the parchment paper and let the cakes cool completely, about 1 hour.
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4
Meanwhile, make the icing: Place the chocolate and butter in a small mixing bowl.
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5
In a small saucepan, heat the cream over high heat until it's just about to boil. Remove the cream from the heat and immediately pour it over the chocolate and butter. Let the mixture sit for about 5 minutes, or until the chocolate is melted, then stir to combine. Don't stir too vigorously or the icing will lose its shine. It should be thick, but still loose enough to pour.
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6
When the cakes are cooled, turn them right-side up on the cooling rack and place the rack over a rimmed baking sheet. Starting with one layer, pour a generous 1/2 cup (120 ml) of the icing over the center of the layer. Use an offset spatula to smooth the icing over the top and down the sides (the rimmed baking sheet will catch your drips). Repeat with the second layer and another 1/2 cup (120 ml) of icing. Top with the third layer and spread some of the remaining icing over the top (you can coat the sides of the cake as well if you like). The icing will become firm as it cools. Use a large spatula to transfer the cake to a serving plate.
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7
The cake can be covered and stored at room temperature for up to 3 days.
