Line a 9x13-inch pan with parchment paper, leaving some overhang.
To start the cookie bars, whisk the flour, cocoa powder, baking soda, and salt in a bowl.
In a separate bowl, use an electric mixer to cream the butter and both sugars until light and fluffy, about 3-4 minutes.
Beat the eggs into the creamed butter one at a time, followed by the vanilla.
Mix in flour mixture on low speed until just combined.
Fold in the dark chocolate chunks.
Press dough evenly into the prepared pan.
Bake for 25-28 minutes, until the edges are set and the center is just firm. Let cool completely in the pan.
To start the frosting, microwave the chopped white chocolate in 30-second intervals, stirring between each, until melted and smooth. Let cool for 10 minutes.
Meanwhile, beat the butter until creamy, about 2 minutes.
Beat in the melted and cooled white chocolate.
Add the powdered sugar, vanilla extract, peppermint extract, and salt. Beat on low until combined.
Add the cream, 1 tablespoon at a time, beating until the mixture is spreadable. Add an extra tablespoon of cream if needed to get the proper frosting consistency.
Fold in the crushed candy canes, reserving about 2 tablespoons for garnish.
Spread the frosting evenly over the cooled cookie base.
Refrigerate for 2-3 hours, until set.
Lift bars from the pan using the parchment overhang. Cut into 20 bars with a sharp knife, wiping the blade between cuts if needed.
Finish by sprinkling with remaining crushed candy canes.