In a small bowl, sift together flour and salt. Set aside.
Place 1 Tbsp. of the granulated sugar, lavender, and lemon zest in a mortar and grind lightly with the pestle.
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 ¼ inch thickness. Cut into shapes (I used a 1 ¾ inch cutter) and place on prepared sheet. Sprinkle with some pure cane sugar if desired, then place in the freezer for 15 minutes.
Preheat oven to 325 degrees.
Bake cookies for 12-14 minutes until lightly browned around the edges. Cool on sheet for 5 minutes, then transfer to wire rack. Can be store in an airtight container for 5 days.
