Preheat oven to 350F. Butter 24 muffin tins.
For the cake, whisk cocoa and 1/2 cup lukewarm water in a small bowl. Whisk the remaining 1/2 cup water with the buttermilk in another small bowl. Sift flour, baking soda and salt into a medium bowl and add cinnamon, cloves and cayenne. Stir to combine.
Using electric mixer, beat both sugars and butter in a large bowl until pale yellow and fluffy (mixture will appear granular), about 5 minutes. With mixer running, gradually add beaten eggs; beat until smooth and fluffy, about 15 seconds. Add cocoa mixture; beat to blend. Add flour mixture and buttermilk mixture alternating in 3 additions, beating to blend after each addition. Divide batter among the muffin tins. Bake for10 minutes or until a toothpick comes out clean.
For the frosting, melt butter in a medium saucepan over medium heat. Stir in sugar, cocoa, espresso powder and salt. Gradually stir in cream. Stir until mixture is very hot and just begins to simmer at the edges. Reduce heat to low; stir 1 minute to let flavors blend. Transfer to medium bowl; stir in vanilla (frosting will resemble chocolate sauce) Chill until just thickened, stirring occasionally, about 1 1/2 hours, or in a bowl set in an ice bath.
To frost the cakes, bring frosting to room temperature. Run a knife around cake sides and invert mini cakes out of the muffin tins. Spread about 1 tablespoon of frosting on the first layer of cake and repeat for the remaining 2 layers of cake.