Preheat oven to 350 degrees F (177 degrees C).
Grease 8×8 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.
Sift the sweet rice flour, cocoa powder, and espresso powder into the bowl. Use a spatula to combine.
Lastly, add the marshmallows and fold into the batter.
Spoon batter into your prepared baking pan. Smooth it out with your spatula.
Optional: Top with extra marshmallows if you have them!
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 20-25 minutes.
Let cool for 15 minutes before serving.