Line the baking sheets with parchment paper. Set aside.
Make the lavender sugar
Blend the dried lavender and sugar in a food processor until the flowers are finely ground. (If you don't have a food processor, you could use a mortar and pestle, instead.) Set aside.
Make the cookies
Whisk together the flour, cornstarch, baking powder and salt in a mixing bowl. Set aside.
In another large mixing bowl, beat the butter with the lavender sugar and lemon zest until it's fluffy and well combined.
Add the egg and the vanilla and mix to combine.
Gradually add the flour mixture and beat until it's crumbly.
Use your hands to squeeze the crumbles until the dough comes together. You may need to add a little more flour, a tablespoon at a time if the dough is too wet. The dough should come together in one piece.
Cut the dough in half and roll it between 2 sheets of parchment paper, about ¼ inch (0.6cm) thick. Then put the rolled out dough in the freezer for 15 minutes.
Meanwhile, preheat the oven to 350°F / 180°C.
Take the dough out of the freezer and use cookie cutters to cut out shapes.
Place the cookies about 2 inches apart on the prepared baking sheet and bake for about 15 minutes, until they're light golden brown on the edges. (I bake them one tray at a time.)
Re-roll the dough scraps and repeat the procedure with the other piece of dough.
Transfer the baked cookies to a wire rack and let them cool completely.
Make the lemon glaze (Optional)
Whisk together the powdered sugar and lemon juice in a small bowl.
Drizzle over the cooled cookies.
Enjoy!
Notes
You can store these cookies in an airtight container at room temperature for up to about a week.
The number of cookies will depend on the size of your cookie cutters.
Don't overbake the cookies or they could get too hard.
Detailed freezing instructions are included in the post.