Preheat oven to 350 degrees F.
Grease 8x8 baking pan with butter and line with parchment paper. Set aside.
Heat the butter over high heat until it melts. Lower the heat to low. Heat the butter until small brown bits start to appear. Remove from the stove.
Add chocolate to a small bowl. Pour the brown butter over the top and stir until all the chocolate melts. Let the mixture cool for 2 minutes.
In a large bowl, combine granulated sugar, brown sugar, eggs, vanilla extract, peppermint extract, and salt. Beat with a hand mixer or stand mixer until thick and creamy (~5 minutes).
While mixing, stream in your chocolate ganache from step 4. Mix until well combined.
Lastly, sift the sweet rice flour and cocoa powder into the bowl. Use a spatula to combine.
Spoon batter into your prepared baking pan. Smooth it out with your spatula.
Bake for 20 minutes.
Take out the brownies and smack them on the counter to get rid of some of the air bubbles. Put them back in the oven and bake for another 10 minutes
Let cool for 15 minutes.
Melt the white chocolate in the microwave and crush up the candy canes. Once the brownies are cool enough, drizzle the white chocolate on top and sprinkle with the crushed candy canes.