Cream BUTTER thoroughly.  Add SUGAR slowly, creaming in thoroughly.  Add FLOUR slowly, blending in thoroughly.  Add VANILLA and mix thoroughly.  (May need to be done by hand as batter is very thick, heavy, and crumbly.) 

Press into ungreased 11x13 pan and bake @ 350 for 20 minutes.  Lower temp to 325 and bake for 20 more minutes.

Cut into bars while warm.  Very rich and yummy!

In Anne of Avonlea, when Anne spends time with her "genius student" Paul, she especially enjoys his grandmother's shortbread.  All of L.M.M.'s books are so full of yummy food that I'm drooling by the time I'm done.  The shortbread sounds exactly like what L.M.M. describes and is a great companion to this (or any!) book.