Mix butter, brown sugar, instant coffee granules and vanilla thoroughly using an electric mixer. Gradually blend in flour and corn starch.
Form into 1-inch balls and place on ungreased baking sheets. Gently press down on each cookie to flatten using fingers or a flat bottomed drinking glass (dipped in sugar to prevent sticking).
Bake in a preheated 300°F oven for 25 to 30 minutes, or until bottoms begin to brown.
Cool for 5 minutes; remove to a wire rack to cool completely. Combine powdered sugar, milk and liqueur; mix until frosting is smooth. (note; if not using liqueur, an additional tablespoon of milk may be needed). Drizzle cookies with frosting.
Recipe note: For European style shortbread, turn dough onto a lightly floured surface and knead until smooth, about 2 minutes. Pat into a 1/3-inch thick rectangle measuring 11 x 8-inches. Cut into 2 x 1-inch strips. Place 1-inch apart on ungreased baking sheets. prick with a fork. Bake as above.