Preheat oven to 325F with the rack in the middle position.
Line an 8 or 9 inch square baking dish with parchment paper, with at least two edges hanging over the dish (this will make it much easier to remove the cookies later).
In a food processor, add the flour, sugar, salt, zest of one lemon, and rosemary. Pulse together a few times to mix.
Slowly drizzle the olive oil into the dough and pulse until just combined and incorporated. The dough will look wet.
Press the dough across the bottom of the baking dish inn an even layer. Prick the dough all over with a fork. If desired, press some additional rosemary leaves into the top of the dough. Sprinkle with a little additional salt across the dough.
Bake until the cookies are just golden brown, approximately 35-40 minutes. (An 8 inch pan may take 5-10 minutes longer as the dough is thicker).
Place the baking dish on a wire rack to cool. While still warm but not hot, remove the bars from the dish using the edges of the parchment paper. Cut into squares, triangles, or rectangles as desired.
To get a firmer, crisper shortbread, use granulated sugar instead of powdered sugar.The lemon is n not obvious in this recipe. If you want to taste the lemon, increase to zest from 2 or 3 lemons.It is important to cut while still warm to minimize breaking and crumbling as the dough is very tender.