Combine sugar, the 2/3 cup butter, coffee, the 1/4 cup coffee liqueur, eggs, melted unsweetened chocolate, and vanilla in a large mixing bowl. Beat with an electric mixer on medium speed for 2 to 3 minutes or until creamy, scraping bowl often. Reduce speed to low; add flour, baking powder, salt, and cinnamon. Beat until combined.
Drop by rounded teaspoons 2 inches apart onto greased cookie sheets. Bake in a 350 degree F oven for 8 to 12 minutes or until edges are firm. Cool on cookie sheet for 1 minute. Remove and cool on wire racks.
Spread Coffee Frosting over cooled cookies. Drizzle with melted semisweet chocolate, if desired. Makes about 60 cookies.
Beat butter (no substitutes), powdered sugar, and coffee liqueur in a medium mixing bowl. Gradually beat in enough coffee to make of spreading consistency.