Preheat oven to 350°F. Line a 9×9-inch baking pan with parchment paper and set aside.
In a large bowl, stir together the melted butter and brown sugar until the mixture is smooth and fully combined.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla and peppermint extract.
In a separate medium bowl, whisk together the flour, cornstarch, baking powder, and kosher salt.
Add the dry ingredients to the butter mixture and stir until no dry streaks remain.
Fold in the white chocolate chips.
Transfer the batter to the prepared baking pan and spread it into an even layer.
Bake for 30 to 35 minutes, or until the top is golden brown and a toothpick inserted into the center comes out with a few moist crumbs, but no wet batter.
Let the blondies cool for about 10 minutes while you prepare the toppings.
Melt the milk chocolate chips in a microwave-safe bowl, heating in 20 to 30 second intervals and stirring between each until smooth. Repeat with the white chocolate chips in a separate bowl.
Drizzle both chocolates over the warm blondies and sprinkle the crushed peppermint candies on immediately so they stick.
Let the blondies cool completely before slicing and serving.