In a large bowl, cream together the butter and both sugars until thoroughly mixed.
Blend in the remaining wet ingredients: egg, vanilla, peppermint extract, and almond butter.
Incorporate the dry mixture: flour, cocoa powder, baking powder, baking soda, and salt. Be sure to spoon and level the flour and cocoa rather than scooping directly from the bag. Mix until fully combined.
Chill the dough in the refrigerator for 30 minutes.
Heat the oven to 350°F (175°C).
Using a medium cookie scoop (about 2 tablespoons) or a spoon, form the dough into balls. Gently dust the tops with crushed candy canes (a light coating is sufficient; you'll add more later).
Arrange on a parchment-lined baking sheet and bake for 10-13 minutes. In my oven, 11 minutes works best, but ovens vary. The cookies will firm up as they cool, so allow them to rest before consuming or applying the melted white chocolate.
Immediately after removing from the oven, use a round cookie cutter slightly larger than each cookie to swirl it around the cookie, creating uniform circles. This is not cutting but shaping while they are still soft, so work promptly.
Microwave the white chocolate in 30-second increments, stirring in between. Drizzle over the cookies and top with the remaining crushed candy canes. Serve and enjoy!