Heat oven to 350°F.
In a large mixing bowl, combine sugar, 2/3 cup butter & 1/3 cup coffee.
Add 1/4 cup liqueur, eggs, melted chocolate & vanilla extract.
Beat at medium speed until mixture is creamy, scraping bowl often.
Add the remaining cookie ingredients.
Reduce speed to low. Beat mixture until well combined.
Drop by rounded teaspoons 2 inches apart onto ungreased cookie sheets.
Bake 8-12 minutes or until set.
Let stand for 1 minute, remove from cookie sheets & allow to cool completely, set aside.
Combine frosting ingredients, except the 3-4 Tbsp coffee, in a medium mixer bowl.
Beat at low speed, scraping bowl often & gradually adding enough coffee for desired spreading consistency.
When completely cooled, frost the cookies with prepared frosting.
Drizzle with melted chocolate chips if you like.