Preheat oven to 350 degrees F and line a 9x13-inch baking pan with parchment paper, set aside.
In a medium saucepan melt the chocolate and butter together over medium-low heat. Set aside.
In the bowl of a stand mixer fitted with a whisk attachment mix the eggs and extra egg white until thick and frothy.
Add the sugar and vanilla and beat again till combined.
Add the melted chocolate mixture and mix until just combined.
In a medium mixing bowl combine the flour, cocoa powder, and baking powder.
Add the dry ingredients into the stand mixer bowl and mix by hand till just combined. Don’t overmix!
Pour into the prepared baking pan and bake for 20-25 minutes until a toothpick comes out clean. Don’t overbake.
Remove the brownies from the oven and cool completely at room temperature then chill in the refrigerator for 30 minutes.
To make the frosting, in a large mixing bowl add the butter and cream cheese. Beat with a hand mixer until light and fluffy.
Add the powdered sugar, peppermint extract, milk, and food coloring. Mix for several minutes until creamy and light.
Spread the frosting over the cooled brownies evenly. Cover with plastic wrap and refrigerate at least 30-60 minutes before continuing.
To make the ganache, combine all the ingredients in a saucepan over medium-low heat, whisking until melted and smooth. Don’t over-warm. Let cool for 5 minutes.
Spread over the chilled frosting layer and sprinkle with crushed candy canes if desired
Refrigerate until the chocolate is set, about 30 minutes.
Cut and serve.