Adjust the oven rack to the middle position and preheat the oven to 350°F. Spray an 8" tart pan with non-stick cooking spray and set aside.
Whisk together the flours and salt in a medium mixing bowl and set aside.
Using a hand or stand mixer, beat the sugar and butter together until fully incorporated and airy, about 1 minute. Add the rosemary, lavender, lemon zest, vanilla and salt to the sugar and butter and mix until incorporated. With the mixer running, slowly add the flour over low speed until just incorporated, scraping down the sides of the bowl as needed. There should be clumps of dough at this point.
Pour the mixture into the prepared tart pan and press down lightly with your hand to smooth the surface. The bottom side of a measuring cup is another good way to pat down the surface. Using the tines of a fork and pressing down so you hear the metal tap against the pan, prick lines of holes in the dough to create a dozen wedges. Finish by pressing the bottom of the tines horizontally around the edges of the dough.
Bake for about 23 minutes or until the edges have just started to turn golden but the center is still pale. Remove from the oven and allow to cool for a few minutes. Then, using a knife or bench scraper, cut the shortbread along the pricked lines. Allow to cool a bit more in the pan and then carefully lift the pieces out using a spatula or cake server and transfer to a wire rack to cool completely.
These cookies are based on Dorie Greenspan's "Rose-Hibiscus Shortbread Fans" Recipe
You can omit the rice flour and use 1 cup plus 2 tablespoons all purpose flour