In a medium bowl, whisk together the flour and salt.
In a large bowl, use an electric mixer to beat the butter and sugar until smooth and creamy. Beat in the egg. Beat in the peppermint and vanilla extracts. On low speed, beat in the flour mixture. Shape the dough into a ball; wrap in plastic wrap and refrigerate for 1 hour.
Preheat the oven to 375°F. Coat baking sheets with nonstick cooking spray (or parchment paper).
Shape the dough into 1 inch balls (roll with your hands) for a total of 36 cookies; place on prepared baking sheets.
Bake 10 to 12 minutes or until the bottoms are lightly browned. Transfer the cookies to wire racks to cool completely.
When cool, drizzle with melted white chocolate; dip in chopped candy canes. Let cool completely to harden.