Melt the butter and chocolate chips together over low heat in a pan on the stove. Stir until smooth and no lumps remain. Remove from heat and let cool slightly.
In a large mixing bowl, mix the eggs and sugar together until well incorporated. Add the vanilla and mix.
Add the cooled chocolate/butter mixture (it's o.k. if it's still slightly warm) and mix with the egg/sugar mixture until well blended.
Add the flour, baking powder, and salt. Mix well.
Pour into a well-greased 9-inch round cake pan. (I highly suggest greasing the pan, then adding parchment paper and greasing that as well).
Bake at 350 degrees F. For 30 minutes, until a toothpick in the center comes out clean. Cool on a wire rack for five minutes. Run a knife around the edge to loosen the cake and then cool for an additional ten minutes.
Invert the cake onto a cake stand or serving platter and cool completely. (Remove the parchment paper if it is stuck to the cake).
Beat the butter and cream cheese together until combined.
Gradually beat in the powdered sugar.
Add the peppermint extract and food coloring and beat until well blended.
Spread on top of cooled cake and refrigerate for 30 minutes.
Heat the cream in a medium-sized pan on the stove over medium-high heat to almost boiling. Remove from heat.
Carefully pour in the chocolate chips, making sure that all of them are covered by the cream. Let sit for five minutes so the hot cream will melt the chocolate chips. Then stir until smooth and glossy.
Refrigerate for 30 minutes or more, until spreadable. Spread over the top (and sides, if desired) of cake.
Refrigerate until ready to serve, or sprinkle with crushed candy canes and then refrigerate.
Note: If making a decorative snowflake design with candy canes, chill the cake for 45 minutes or longer to give the ganache time to set up.