To begin, preheat your oven to 350 and spray a pan with no-stick spray.
To a large mixing bowl, add you butter, brown and white sugars. Using a mixer, beat them together till creamy. Add the vanilla, lemon zest, lemon juice, and egg and blend in briefly.
To the same bowl, add your flour, cornstarch, lavender, baking soda, and salt. Mix together till you have a thick, smooth cookie dough batter.
Using a medium cookie scoop, space your cookies out onto your pan evenly (for no more than 12 cookies per pan). Bake in the oven for 10-12 minutes, or till the edges are set and getting color.
Let cool entirely, before drizzling or spreading the lemon glaze on top.
To a mixing bowl, add your powdered sugar, lemon juice, and milk. Whisk together till well combined and you have a consistent glaze.
Drizzle or spread onto your cookies. Sprinkle a little extra dried lavender on top.
Devour!