For Cookies:

In the bowl of your stand mixer cream together the butter and sugar until fluffy.
Next beat in the egg, ground coffee, and vanilla extract.
Mix until well combined.
Carefully mix in the flour, baking soda and salt until just combined.
Remove dough from bowl and cover dough with plastic wrap. Refrigerate for at least 12 hours.
Preheat your oven to 350°F.
Form 36 dough balls (about a heaping tablespoon) and place them 2-3 inches apart on a lined baking sheet.
Bake for 12-16 minutes or until the edges of the cookie are golden brown.
Allow cookies to slightly cool on the baking sheet then transfer them to a wire rack.
For the frosting:

In a large bowl cream, the butter until light, fluffy, and pale.
In a tiny bowl dissolve the instant espresso in the heavy.
Slowly beat in the powdered sugar and coffee-milk mixture.
Mix until the frosting is light and fluffy (3-5 minutes).

Once cooled frost cookies and garnish with espresso beans.