Preheat oven to 400 degrees. Lightly spray a baking sheet with nonstick baking spray with flour.
In a large bowl, sift together flour, 1/3 cup sugar, baking powder, baking soda, and salt. Using a pastry blender, cut in butter until mixture is crumbly. Stir in white chocolate morsels and peppermint baking chips.
In a small bowl, whisk together buttermilk, egg yolk, vanilla extract and peppermint extract. Add buttermilk mixture to flour mixture; mix until dough comes together in moist clumps. Gather dough into a ball and knead for 2 to 3 turns. Place on a lightly floured surface and pat to about 1/2-inch thickness.
Using a 4-inch cutter, cut out dough (cut straight down, do not twist). Transfer to prepared baking sheet, spacing 1 inch apart.
Whisk 1/4 cup water with 1 egg and brush over tops of scones. Lightly sprinkle scones with remaining tablespoon of sugar. Bake scones for 18 to 20 minutes, or until light golden brown. Serve with Candy Cane Cream, if desired.
Candy Cane Cream:
In a medium bowl, beat cream and candy canes at medium speed with an electric mixer until medium peaks form. Garnish with mint leaf and crushed peppermint candies, if desired.