Mix the sugar, lemon zest and ground lavender together in a small bowl. Set aside.
Preheat your oven to 350 degrees. Line two cookie sheets with parchment paper and set aside.
In a large bowl, whisk together the flour, baking powder and salt. Then set aside.
In a large bowl cream together the butter and granulated sugar together with an electric mixer on high speed until fluffy, about two minutes. (You can also use a stand mixer fit with a paddle attachment.)
Add in the egg, vanilla, lemon zest and dry lavender and mix on medium speed until pale in color and fluffy, 1-2 minutes.
Slowly add in the dry ingredients. Mix on low speed just until the dough pulls together.
Scoop the dough into balls with a small cookie scoop. Roll into balls, then roll in the lemon lavender sugar.
Place the dough on to the prepared baking sheet and slightly flatten each ball. (Bake 8 cookies at a time.)
Bake the cookies for 8-9 minutes. Let them cool on the baking sheet for 5 minutes, then transfer them to a cooling rack to finsih cooling.
In a small bowl, mix the powdered sugar and lemon juice together until a thick glaze forms. It should drizzle off a spoon easily, but not be super runny.
Once the cookies are cooled, drizzle icing over them. Allow the icing to harden on the cookies and then enjoy!
