Preheat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line it with parchment paper, leaving an overhang on both long sides.

In a large bowl, whisk the melted butter and sugar together vigorously for about 30 seconds, until pale and glossy.

Whisk in the eggs one at a time, then the vanilla extract and peppermint extract.

Sift the cocoa powder, flour, salt, and baking powder over the wet mixture. Fold gently with a spatula just until no dry streaks remain. The batter will be thick.

Fold in half the chocolate chips and half the crushed candy cane pieces.

Pour the batter into the prepared pan and smooth the top. Sprinkle the reserved chocolate chips and candy cane over the surface, pressing lightly.

Bake for 42–45 minutes, checking at the 40-minute mark. The loaf is done when the top is matte and crackly and a toothpick comes out with a few moist crumbs, not wet batter.

Let the loaf cool in the pan for 10 minutes, then transfer to a wire rack to cool completely, about 1 hour.

Whisk together the powdered sugar, heavy cream, and peppermint extract until smooth. Drizzle over the cooled loaf and top with the remaining crushed candy cane while the glaze is still wet.

Slice with a sharp knife once the glaze has set, about 15 minutes.