To prepare cake, preheat oven to 350F. Grease three 5-inch cake pans and line bottoms with parchment paper. Set aside.
In a large bowl, mix together sugar, flour, cocoa powder, baking powder, baking soda and salt.
Crack in the egg, spoon in the sour cream, and pour in the oil and the vanilla. Mix with a wooden spoon until just combined.
Pour in the boiling water, and slowly mix until smooth and liquidy.
Divide batter evenly among the prepared cake pans. Bake for 18 to 20 minutes. Remove from oven and let cakes cool completely.
Run a pairing knife around the edge of the cake to loosen it from the pan. Peel off the parchment paper circles.
To prepare buttercream, beat butter for a few minutes in a standing mixer with the paddle attachment on medium speed. Add powdered sugar and turn the mixer on low, beat until the sugar incorporates with the butter. Add vanilla, heavy cream and cocoa powder, beat on medium speed for another 3 minutes, or until buttercream becomes light and fluffy.
To assemble the cake, place one cake layer on your serving plate and spread with 1/4 cup of the buttercream. Place another cake layer on top, and gently press down a little bit. Spread with another 1/4 cup of the buttercream. Place the last layer of cake on top, smear the remaining buttercream on the top and sides of the cake. Cover and refrigerate.
To prepare ganache, place the chocolate and heavy cream in a medium heatproof bowl over a pot of simmering water. Stir the mixture using a wooden spoon until melted and smooth, about 5 minutes. Let cool slightly.
Remove cake from the refrigerator. Pour ganache over the top of the cakes. Use an offset spatula to gently push the ganache over the sides of the cake to create the dripping effect.
Scatter sprinkles on top of the ganache and gently press some on the sides of the cake.