In a large bowl or stand mixer fitted with a paddle attachment, beat the butter and sugars together on medium high speed until fluffy and light in color, about 2-3 minutes.
Add the egg and extracts, and then mix on high speed until combined, scraping down the sides as needed.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, espresso powder, and salt. Add the dry ingredients to the wet and mix on low speed until combined. Add the chocolate and peppermint chips and mix until just combined. The cookie dough will be thick and very sticky. Cover dough tightly and chill in the refrigerator for at least 3 hours.
Remove cookie dough from the refrigerator and allow to sit at room temperature for 10 minutes to make the dough easier to scoop and roll.
Preheat oven to 350°F and line large baking sheets with parchment paper or silicone baking mats. Set aside.
Use a medium cookie scoop or tablespoon to make 1-inch dough balls. Place on prepared baking sheet, 2 inches apart.
Bake the cookies for 11-12 minutes or until the edges appear set and the centers still look soft.
Cool cookies for 5 minutes on the baking sheet, and then transfer to a wire rack to cool completely.
Melt the white chocolate or almond bark according to the package instructions. Dip each completely cooled cookie halfway into the white chocolate and place onto a wax paper-lined baking sheet or cutting board. Sprinkle crushed candy canes on top of the chocolate. Repeat with the rest of the cooled cookies. Place the baking sheet into the refrigerator to help the chocolate set, then enjoy!