Heat the cream and peppermint extract in a small saucepan over medium-high heat. Place the white chocolate chips in a small bowl. When cream begins to boil, remove from the heat and pour over the chips. Let stand for 30 seconds for chocolate to begin to melt, then stir or whisk until smooth. Set aside.

Add the melted dark chocolate to the dough and mix on low speed until fully combined and no butter chunks are visible.

Line two baking sheets with parchment paper.

Use a cookie dough scoop or spoon to drop 24 portions of dough onto the prepared baking sheets, using about 1 tablespoon for each, spacing them 2 inches apart. The batter will be loose and tacky.

Freeze the cookies for 10 minutes while the oven preheats.

Preheat the oven to 350°F.

Remove cookies from freezer. With clean hands, press the dough down into flat, round disks.

Bake the cookies on upper-third and lower-third racks of oven, switching pan positions halfway through cook time, until risen and no longer wet in the center, about 10 minutes.

Check to see that cookies are done. Remove from oven or add time as needed.

Using a spatula, transfer the cookies to cooling racks and let cool completely, 20-30 minutes.

Chop the candy canes into small pieces, or use a food processor and pulse candy canes a few times. Pour the crushed candy onto a plate and spread into an even layer.

Invert half of the cooled cookies so they're flat-side up. Using a spoon or offset spatula, spread each with 1 teaspoon of the white chocolate ganache. Top with the remaining cookies, keeping the flat sides together. Squish each cookie sandwich so the ganache is visible on the edges. Roll edges of cookies in the crushed peppermint so it sticks to the ganache.

Serve immediately, or store in an airtight container at room temperature for up to three days, or chill in the refrigerator for one week.