Preheat oven to 400F. Line a large baking pan with parchment paper. Set aside.
In a medium bowl, combine the flour, sugar, baking powder, and salt. Set aside.
Cut in butter with using a pastry cutter or two forks until mixture resembles coarse sand. **Alternatively (and a much easier method), freeze one stick of butter for about 30 minutes. Remove from freezer and grate butter using the largest holes on a cheese grater. Add to flour mixture and stir to combine. Set aside.
In a medium bowl, whisk egg, peppermint extract, vanilla extract, and milk.
Make a well in the dry ingredients and pour wet ingredients in. Fold until just combined. Add more flour if dough is too sticky. If dough is too dry, add 1-2 tablespoons of milk.
Turn dough out onto prepared pan and shape into a 7-inch disk. Cut dough into 8 wedges, but do not separate pieces.
Bake for 16-8 minutes, or until scones are golden brown.
Let cool for 10 minutes on pan, then move to a wire rack to cool completely.
To make the glaze, in a small bowl, microwave white chocolate wafers (or chips) on medium power until wafers are melted and smooth, stirring ever 15 seconds so not to burn.
Remove from microwave and drizzle or spread onto cooled scones. Sprinkle with crushed candy canes.