Preheat your oven to 350°F / 180°C / gas mark 4. Line two baking sheets with parchment paper.
In a small bowl, whisk together the flour, cornstarch, and baking powder.
Cream together the butter and sugar along with lemon zest and dried lavender until light and fluffy.
Mix in one large egg until very well combined.
Gradually add in your dry flour mixture until just combined.
Use a small cookie scoop to drop tablespoon-sized balls of dough onto your prepared baking sheets.
Gently flatten each ball until they are about one-third inch thick.
Bake for about 12 to 15 minutes until centers are just set and edges appear slightly golden.
Let cookies cool on the baking sheet for five minutes before transferring to a wire rack.
Whisk together sifted powdered sugar with fresh lemon juice and optional lavender extract until thick but pourable.
Spoon glaze over each cooled cookie and sprinkle with additional lavender buds or lemon zest if desired.
Store leftover cookies in an airtight container at room temperature for up to four days.