Start by making the shortbread. Cream butter and brown sugar. Add in flour and mix well. Either turn dough to floured board or knead right in the bowl,adding a pinch or two of flour.
place dough on cookie sheet. Roll out entire amount until about a half inch thick. Score the pieces into 2 inch by 2 inch. Each cube should be pricked twice by a fork, to allow for vapor to escape. Bake for 30 minutes in a 325 oven.... they should be lightly toasty bottomed when ready. Cool 10 minutes and transfer to a wire rack over a larger pan.
In a blender or food processor crush the peppermint candy... it is okay for some to be powdery and others small chunks. Set aside.
In a double boiler pan, melt the chips along with the peppermint extract. Keep stirring, it will ceaze up quickly if you turn away. Quickly pour and spread over cookies and dust with the crushed peppermint. Refridgerate. These were best the second night and beyond, as the shortbread set better and the topping was crisp and cool.