In a separate bowl, whisk together flour, instant espresso powder, baking powder, baking soda and salt. Set aside.
In a stand mixer fitted with a paddle attachment, cream together the browned butter and sugar until light and fluffy (3-4 minutes). Scrape the sides and bottom of the bowl.
Beat in cocoa powder until well combined. Scrape the sides and bottom of the bowl.
On low-medium speed, beat in eggs and vanilla extract one at a time, until each is well incorporated. Scrape the bottom and sides of the bowl.
Add dry ingredients to the wet 1/2 at a time. Mix on lowest setting until JUST combined. Do not overmix.
Gently fold in the chopped chocolate bark and/or chocolate chunk pieces.
Cover the mixing bowl with pastic wrap. Chill in the fridge at least 2 hours and up to overnight.
When it's time to bake the cookies, preheat the oven to 350 F (177 C). Line 2 large cookie sheets with parchment paper. Pull the cookie dough out to sit at room temperature for about 25-30 minutes. Scoop dough out using a 2" cookie scoop with trigger release onto a parchment lined baking sheet. Leave about 3" (in) in between each cookie. They are meant to spread a bit while baking. Top each cookie dough ball with pieces of chopped peppermint bark.
Bake at 350 F ( 177 C) for 12-16 minutes or until cookies are set around the edges. The center may still look slightly underbaked.
Pull cookies from the oven, cool on the cookie sheet placed on top of a cooling rack for 5 minutes.For perfectly circular cookies, use the inside large pastry ring to gently nudge the edges of the cookie back into a circular shape.
Using a spatula, gently remove cookies from the pan, onto a cooling rack to finish cooling.