Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper.
Melt the butter and dark chocolate together in a microwave-safe bowl or saucepan until smooth. Let cool for 2 to 3 minutes.
Whisk in the granulated sugar and brown sugar until glossy and fully combined.
Add the eggs and egg yolk one at a time, whisking well after each addition.
Stir in the vanilla extract, peppermint extract, and espresso powder.
In a separate bowl, whisk together the flour, cocoa powder, and salt.
Fold the dry ingredients into the wet ingredients just until combined. Do not overmix.
Fold in the chocolate chips.
Spread the batter evenly into the prepared pan.
Bake for 30 to 33 minutes, or until a toothpick inserted near the center comes out with moist crumbs attached.
Allow the brownies to cool completely in the pan.
To make the ganache, place the chocolate chips in a heatproof bowl.
Heat the heavy cream until steaming but not boiling. Stir in the espresso powder.
Pour the hot cream over the chocolate chips and let sit for 2 minutes.
Add the butter and peppermint extract. Whisk until smooth and glossy.
Spread the ganache evenly over the cooled brownies.
Sprinkle with crushed candy canes and chocolate curls if desired.
Refrigerate for 15 to 20 minutes to set the ganache.
Slice into 16 brownies and serve.