Combine coffee and milk in a french press the night before you plan to make this dessert, and place unpressed french press in fridge overnight (12-24 hours).
After soaking, press french press to pour out coffee milk.
Prepare a batch of Perfectly Chewy Chocolate Chip Cookies and let cool (link to recipe in blog post above, or search "Chocolate Chip Cookies" on www.flourdeliz.com. Allow cookies to cool completely.
Beat butter in a small bowl till soft and whipped.
Add powdered sugar and prepared coffee milk, and beat until frosting is of desired consistency. Add more coffee milk if too thick, or more powdered sugar if too thin.
Pipe or spread frosting onto the bottom of one cookie, and press the bottom of another cookie against the frosted side.
Eat as a sandwich and enjoy!