My favorite is Laurie Colwin's. And the secret to "sandi" texture just might be the rice flour.
Cream:
1/2 C unsalted soft butter
1/4 C powdered sugar
1/2 tsp pure vanilla
Fold in
3/4 C all-purpose flour
1/4 C rice flour
1/8 tsp baking powder
1/8 tsp salt
Colwin's states that the rice flour gives the cookie its slight crunchy/crumbly-ness. I agree and make a point of using it. However, if you don't have the rice flour, just use 1 cup of regular flour.
Dough will be very soft. Gently pat into 8" circle on an ungreased cookie sheet. Score 6-8 wedges and then press the tines of a fork along the lines.
Bake 375 degrees for 20 minutes or until lightly brown around the edges. Cut with a knife along the lines while warm.
I usually add some minced dried cranberries (pretty when cut into heart shapes) or minced dried apricots... but this is definitely gilding the lily.
When you're all done, make a pot of tea, pull up a comfy pillow, and watch "Random Harvest" while enjoying the fruits of your labor. Pretend you're Greer Garson nibbling on shortbread and trying to not fall in love with Ronald Colman. If you've added lightly toasted and finely chopped pecans, pretend you're Scarlett O'Hara nibbling on pecan shortbread at Tara, trying not to fall in love with Rhett Butler.
PS: I think these taste a lot like Walker's shortbread.
PPS: Try this first, then use regular sugar instead of the powdered sugar for more "sandyness". However, I can't validate that method.