Process the flour, butter, sugar, egg white, lemon zest, and lavender in a food processor until a dough begins to form.
Form the dough into a 1x2-inch thick rectangular log. Wrap in parchment and chill for 20 minutes.
Preheat oven to 350. Line a baking sheet with parchment paper.
Slice the dough into ¼ inch thick circles. Place on the prepared baking sheet.
Bake for 16-18 minutes or until golden brown. Let cool completely.
Stir together the ingredients for the glaze.
Hold a cookie over the bowl of glaze. Spoon glaze to cover one half of the cookie. Let the excess drip off. Place on the parchment. The glaze will harden.
Notes
Lavender - Culinary grade dried lavender buds can also be used if you don't have access to fresh.