Preheat the oven to 180°C (350°F) and line a 20cm (8-inch) square baking pan with baking paper.

In a large bowl, whisk the eggs, vanilla extract, and peppermint extract until foamy. Add the dark brown sugar and melted butter, whisking until fully combined.

Sift the cocoa powder and gluten-free flour into the bowl. Gently whisk until the batter is thick and smooth. Fold in the chopped dark chocolate. Pour the batter into the prepared baking pan, spreading it out evenly.

Bake for 20 minutes or until the top is set but still soft. The brownies should feel firm to the touch but remain fudgy inside. Allow to cool completely.

To make the dark chocolate peppermint ganache, place the chopped dark chocolate in a glass bowl. In a small microwave-safe bowl, heat the coconut milk until warm but not boiling. Stir the peppermint extract into the warm coconut milk, then pour it over the chopped chocolate. Let it sit for 5–10 minutes before stirring with a metal spoon until smooth and glossy.

Pour the ganache over the cooled brownies, smoothing it out with a spoon or offset spatula. Sprinkle the crushed candy canes over the top. Refrigerate until the ganache is set.

Slice into squares and enjoy!