Stir together the instant espresso and water. Set aside.
In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the butter, granulated sugar, and brown sugar together on medium speed until fluffy and light in color, about 2 minutes. Add the egg, egg yolk, vanilla extract, and peppermint extract, and beat on high speed until combined. Scrape down the sides and bottom of the bowl as needed.
With the mixer on low speed, slowly add the flour, cocoa powder, baking soda, and salt. Beat on low until combined and then beat in the chocolate chips and peppermint crunch. The cookie dough will be thick and sticky. Cover dough tightly and chill in the refrigerator for 1 hour or up to 3 days. Chilling is mandatory.
Remove the cookie dough from the refrigerator and allow to sit at room temperature for 15 minutes (if refrigerated longer than 1 hour). Preheat the oven to 350ºF. Line large baking sheets with parchment paper or silicone baking mats. Set aside.
Scoop and roll the dough, 2 Tablespoons of dough for each, into slighter taller than wide balls. Arrange 6 on each baking sheet. The cookie dough will still be stick, so wipe your hands after forming a few to make it easier.
Bake for 10-12 minutes until the edges are set and the centers are slightly soft.
Allow the cookies to cool for 5 minutes on the baking sheet before transferring to a wire rack to cool completely. If desired, garnish with crushed peppermint crunch.