For the scone: Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
In a bowl, combine the flour, crushed candy canes, sugar, baking power, salt and baking soda. Using 2 knives or a pastry blender, cut in the butter until the butter is in small pieces but still visible. Stir in the buttermilk. Knead lightly just until the dough holds together.
Divide the dough into 2 pieces. Form each piece into a disc about 8 inches wide and 5/8 inch thick. Cut each disc into 6 wedges and place on the prepared pan. Bake until light golden, 20 to 25 minutes. Remove to a cooling rack and let cool completely.
For the ganache: In a pot, bring the cream and corn syrup to a simmer, then remove from the heat. Add the white chocolate melts and peppermint oil and stir until completely melted. Transfer to a bowl if necessary for ease of dipping.
Dip the scones in the ganache as desired, returning them to the parchment to collect any ganache that drips off. If decorating with sprinkles, sugar or candy, add them quickly before the ganache sets, decorating one at a time as each scone is dipped in the ganache.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.