Preheat oven to 350 degrees F. Spray four 6-inch pans or three 8-inch round cake pans with nonstick spray, line the bottom of the pans with parchment paper and spray again. Set aside.
Using a double-boiler or microwave safe bowl, melt the white chocolate. Set aside for a minute.
Whisk together the flour, salt, and baking powder. Set aside.
In the bowl of an electric mixer, fitted with a paddle attachment, cream the butter and sugar on medium high speed for about two minutes, until light and fluffy.
Turn the mixer to medium and add the eggs, yolks, vanilla, peppermint and melted white chocolate. Stop the mixer and scrape down the sides and bottom of the bowl. Mix again until well blended.
With the mixer now on low, alternately add the dry ingredients and the buttermilk, starting and finishing with the flour mixture. This helps your ingredients to blend evenly.
Pour the batter into prepared pans (about 12 ounces in each 6-inch pan and about 16 ounces in each 8-inch pan). Bake for about 20 to 22 minutes, until a toothpick inserted in the center comes out with just a few moist crumbs on it.
Let the cake layers cool about 10 minutes in the pans and then invert onto a wire rack to cool completely.
When the cake layers are cooled completely, level if needed, and then wrap in plastic wrap and freeze for at least an hour.