Preheat the oven to 350°F. Butter and flour an 8-inch cake pan.
In a large mixing bowl, mix together the sugar, salt and lemon zest – use your fingers to rub the mixture together until you can really smell the lemon zest.
Add the butter and use an electric mixer to blend until well combined and fairly smooth; it won’t get very fluffy. Add the vanilla and blend, then add the flour and mix on low just until combined. The dough should be soft and crumbly, and should just hold together when squeezed in the palm of your hand.
Transfer the crumbly dough into the prepared pan. Pat the top as smoothly as possible, and then use a spice jar to roll the top gently until smooth, or pat it smooth with the bottom of a glass.
Use the tines of a fork to score the dough into wedges. Use the back of the tines of a fork to make a border around the edge of the shortbread (see above for step-by-step photos).
Bake for 25 minutes. The shortbread will be very pale when it is done, barely more golden than it was before baking, with the edges ever so golden.
Cool the shortbread in the pan on a wire rack. Either cut the shortbread into triangles in the pan, following the scored lines, or carefully turn the shortbread out of the pan, then carefully clip it right side up onto a cutting board and slice along the scored lines.
Notes
Don’t overwork the dough, or the shortbread won’t be as tender
Make sure the butter is soft, but not melted so that the shortbread retains its firm structure
Make sure to refrigerate the dough before baking. This will allow the shortbread to bake up a little flaky, with a deep bite and also allow the flavor to meld a bit.
Use your fingers or a spice jar to flatten the surface of the dough before baking which will give it a more polished appearance and encourage more even baking.
Score (create lines for cutting the shortbread after baking) and dock (poke tiny holds in the surface) the dough before baking to prevent bubbles and buckling from occurring. These holes allow steam to escape.