Browning the butter gives this shortbread a toastiness which sets it apart from other shortbread recipes. I usually double this recipe. The preparation time doesn't include the chilling of the browned butter.
In a heavy two-quart saucepan, melt all the butter over low heat. Cook butter 8 to 12 minutes, stirring consistently, until butter solids at bottom of pan are a rich brown color and butter has a nutty aroma. Be careful not to burn the butter.
Pour browned butter into a bowl; refrigerate until almost firm, about a half hour.
In large bowl, with mixer at medium speed, beat sugar with cooled browned butter.
Mix flour and salt into butter mixture by hand -- don't overwork the dough. It will be crumbly.
Pat shortbread crumbs into pan of choice. I like to use a square pan.
Bake shortbread 40 to 45 minutes, until browned around the edge. Watch carefully lest they burn. Let cool in pan on wire rack 10 minutes.
Remove shortbread from pan to cutting board. While still warm, cut the whole in half, in half again, and in half again until you have small squares. These are rich, and shouldn't be large.