Preheat oven to 300° F, and position a rack in the center of the oven. Beat the butter, sugars and salt on medium speed (in a stand mixer or with a hand-held mixer) until very fluffy and well blended. Gradually sift the flour(s) and cornstarch, if using, over the top of the butter mixture while stirring.
Lightly knead the dough to form a ball. Firmly press it into an 8x8 pan or shortbread mold, and pierce the dough deeply with a fork several times. (This prevents the shortbread from puffing up). Bake at 300° for 40-50 minutes, until pale gold and just slightly darker at the edges. Allow to cool until barely warm, and cut the shortbread to form bars. Let stand until completely cool (if that’s possible).
Notes
If desired, substitute 1/3 cup of rice flour or cornstarch for an equal amount of all-purpose flour (easiest way to do this is to measure out the 1 ½ cups of flour and then scoop out 1/3 cup and put that 1/3 cup back in the flour bag. Then add the remaining flour to your shortbread as directed).