I don't have any recipes from my Grandma but here is a very old traditional recipe for shortbread.

I make it every year. Last season I made 18 pounds of it.

One pound of sugar
two pounds of butter
three pounds of flour
two teaspoons of salt

Cream the butter and sugar until very light and fluffy
Fold in the flour and salt.

Roll out to about 1/4 inch thick
dock it well
cut into rectangles

bake at 325 until it just starts to turn golden at the edges.

And don't bother halving the recipe or you'll only find yourself making another batch.