If peppermint isn't your favorite, there are many different flavored extracts that would be equally delicious in the frosting on this cake. Besides hazelnut and coffee, orange, raspberry or even maple extract can transform the recipe into something different each time you make it. Look for extracts (we like Boyajian brand) in supermarkets and specialty food shops.
How to Make It
MAKE THE CAKE: Preheat the oven to 325°. Butter three 9-inch round cake pans. Line the bottoms with parchment paper, butter the paper and dust the pans with cocoa, tapping out any excess.
In a small saucepan, melt the coarsely chopped chocolate with the butter over low heat; let cool.
In a medium bowl, whisk the flour with the salt. In a large bowl, using an electric mixer, beat the egg yolks with 1 cup of the sugar at medium speed until light and fluffy, about 3 minutes. Add the cooled chocolate and the vanilla and beat until blended. Gradually beat in half of the milk. In a bowl, dissolve the baking soda in the remaining milk; add this to the chocolate batter along with the remaining 2 cups of sugar and beat at medium speed until combined. Beat in the dry ingredients at moderately low speed.
Pour the chocolate batter into the prepared pans. Bake the cakes on the lower and middle racks of the oven for 35 minutes, or until a toothpick inserted in the centers comes out with a few moist crumbs attached. Let the cakes cool in the pans for 5 minutes. Run the tip of a knife around the inside rim of the pans and invert the cakes onto wire racks. Peel off the parchment paper, then invert the cakes again and let them cool completely.
MAKE THE FROSTING: Put the chocolate in a large heatproof bowl. In a small saucepan, bring the cream to a boil. Pour the hot cream over the chocolate and let stand for 5 minutes, then whisk until smooth. Whisk in the butter and peppermint extract. Transfer half of the ganache to a large bowl and refrigerate it for 15 minutes, or until barely set and slightly cool. Using an electric mixer, whip the chilled ganache at medium speed until thick, creamy and pale, about 3 minutes.
Place 1 cake layer upside down on a cake plate. Spread the top of the cake with half of the whipped chilled ganache. Top with another cake layer and spread with the remaining whipped ganache. Set the third cake layer on top. Spread most of the reserved unwhipped ganache on the top and side of the cake and refrigerate until just set, about 10 minutes. Spread the remaining unwhipped ganache all over the cake. Press the nonpareils around the bottom edge of the cake and press more nonpareils onto the top in a snowflake pattern. Refrigerate the cake for 20 minutes before serving.