Preheat oven to 350 degrees F.
Place parchment paper or silpat mats on 2 cookie sheets.
Add all-purpose flour, unsweetened cocoa powder, baking soda, fine sea salt, and instant espresso powder to mixing bowl. Whisk to combine. Set aside.
Add unsalted butter, granulated sugar, and brown sugar to stand mixer. Beat on medium speed until smooth and creamy, about 2 minutes.
Add egg and beat on low until well combined.
With mixer on low speed, begin adding dry ingredients about 1/4 cup at a time. Scrape the bowl down, if necessary. Beat just long enough for the cookie dough to come together.
Fold in the milk chocolate chips and semisweet chocolate chips.
Using a small cookie or ice cream scoop, drop rounded cookie dough on prepared cookie sheets about 2-inches apart.
Poke caramel pieces into top of cookies.
Bake for 10-12 minutes in preheated oven.
Remove cookie sheets from oven and place on wire rack. Remove cookies from cookie sheets and cool completely.