In large bowl, whisk together flour, cornstarch, salt, baking powder, and baking soda until well combined; set aside.
In a separate large bowl, beat together brown sugar, granulated sugar, and 1 cup butter with an electric mixer on medium speed until well combined. Add egg, egg yolks, and 2 teaspoons vanilla, and beat until well combined.
Beat flour mixture into wet mixture until combined. Stir in cocoa powder and melted chocolate until combined.
Using a small ice cream scoop (about 2 teaspoons), ball up dough. Place on lined baking sheets (parchment, wax, or silpats), cover dough with plastic wrap, and refrigerate 2-3 hours, or overnight, or up to 2-3 days.
Preheat oven to 325 degrees F. Bake cookies in batches about 13-16 minutes or until slightly browned around edges.
Meanwhile, place white chocolate, heavy cream, corn syrup, and peppermint extract in microwave safe bowl. Microwave on high for 30 second intervals, stirring after each interval, until smooth. Cool slightly then stir in half of crushed candy canes. Spread ganache between two cookies. If filling seems a little thin and runny, refrigerate until thicker consistency.
Roll cookies in remaining half cup of crushed candy canes.
SNAPPY TIPS: I strongly suggest refrigerating the dough for best results and not baking right away.SNAPPY SUBSTITUTIONS: I do not suggest substituting margarine for butter, whole eggs for the egg yolks. Results will vary a lot the more you substitute. You can substitute crushed peppermint starlight mints for the candy canes.
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