Add butter to a stand mixer fitted with a paddle attachment and beat at medium speed for 1-2 minutes. Add lemon/lavender sugar, remaining granuated sugar and vanilla and beat for 2 minutes until light and fluffy. Add dry ingredients to butter mixture until it forms a dough. Shape into a disk and wrap tightly in plastic wrap. Refrigerate for 30 minutes.
Line a large baking sheet with parchment paper. Set aside. Roll the dough out to 1/4 inch thickness. Cut into shapes (I used a 1 3/4 inch cutter) and place on prepared sheet. Sprinkle with some pure cane sugar if desired, then place in the freezer for 15 minutes.
Make sure to measure your flour correctly. Do not scoop one entire cup from your flour container or you will have more than the one cup because the flour will be packed and your dough will be dry. Spoon the flour into your measuring cup and level it off with a knife.
The recipe calls for one teaspoon of grated lemon zest, but you can add up to two teaspoons for more lemon flavor.
The amount of cookies will depend on the size of your cookie cutter.
Since everyone's oven temperature differs a bit, bake your cookies until you see the edges begin to lightly brown. Mine took about 14 minutes.