Preheat your oven to 350°F / 180°C / gas mark 4. Lining your baking sheets with parchment paper helps prevent sticking and makes cleanup easier.
In a small bowl, whisk together the flour, cornstarch, and baking powder.
Cream together the butter, sugar, lemon zest, and lavender on medium speed until light and fluffy—about 2 to 3 minutes.
Mix in one large egg until it's very well combined.
Gradually add in your flour mixture until just combined.
Drop rounded tablespoons of dough onto your prepared baking sheets, spaced about two inches apart.
Gently press down each ball of dough until they're about one-third inch thick.
Bake the cookies for approximately 12 to 15 minutes until their centers are just set and edges are lightly golden brown.
Allow the cookies to cool on the baking sheet for five minutes before transferring them onto a wire rack.
Whisk together the sifted powdered sugar with fresh lemon juice and lavender extract if using.
Generously spoon glaze over each cooled cookie and garnish with lavender buds or lemon zest if desired.
Store any leftovers in an airtight container at room temperature for up to four days.