1 1/2 cups all-purpose flour
1/2 cup brown rice flour or cake flour
1 cup powdered sugar
2 teaspoons dried food-grade lavender buds, crushed (a mortar and pestle works well)
1 cup butter, chilled
3 tablespoons very finely minced crystallized ginger
Preheat oven to 350°F.
Line 2 (8-inch) round cake pans with parchment paper so that it comes up over the sides of the pans. Set aside.
In a large mixing bowl, place both flours, powdered sugar, salt and crushed lavender. Stir to mix. Cut butter into small cubes and add to dry ingredients in bowl. Use hands to mix until crumbly. Add ginger and continue to mix with hands until mixture comes together. Gather dough together and place on a work surface. Divide dough in half.
Pat each half into prepared pans. Flute the edge of each with your fingers. Pull out of the pan by holding edge of parchment paper. Place on work surface. Prick each round all over with a fork, then score with a sharp knife into 8 wedges. Pick up each round with parchment and place back into baking pans. Sprinkle 1 1/2 teaspoons of sugar over dough in each pan.
Bake in preheated oven for about 20 to 30 minutes or until golden brown on top. Remove from oven and immediately sprinkle remaining sugar over baked shortbread, 1 1/2 teaspoons on each.
Cool on wire rack. (The smell of warm butter, sugar, ginger and lavender will be seductive and you'll want to start eating the warm shortbread. But don't. The shortbread will taste best when it reaches room temperature.)
Remove shortbread from pans by pulling up on the parchment paper. Use sharp knife to cut the shortbread where it was scored, forming a total of 16 wedges.