Preheat your oven to 350°F (180°C / gas mark 4) and line two baking sheets with parchment paper.

In a small bowl, whisk together the all-purpose flour, cornstarch, and baking powder. Set aside for later use.

In a large mixing bowl, using a stand mixer fitted with the paddle attachment (or a handheld electric mixer), beat the butter, granulated sugar, lemon zest, and dried lavender on medium speed until the mixture becomes light and fluffy—this should take about 2 to 3 minutes. Scrape down the sides of the bowl as needed.

Beat in the egg until fully incorporated and the mixture is smooth.

Reduce the mixer speed to low and gradually add the flour mixture. Mix until just combined. The dough may appear slightly dry but should come together easily.

Using a small cookie scoop or tablespoon, form balls of dough (about 1 tablespoon each) and place them on the prepared baking sheets. Leave about 2 inches (5 cm) of space between each dough ball.

Using the palm of your hand, gently press each dough ball to flatten it to about ⅓ inch (1 cm) thick.

Place one baking sheet in the oven at a time and bake for 12 to 15 minutes, or until the centers are just set and the edges begin to turn lightly golden.

Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

In a medium-sized bowl, whisk together the sifted powdered sugar, fresh lemon juice, and optional lavender extract. The glaze should be thick but still pourable. Add a few drops of purple food coloring if desired, and mix until evenly tinted.

Spoon the glaze over each cooled cookie. Optionally, sprinkle with dried lavender buds and a touch of lemon zest for garnish. Allow the glaze to set for at least 30 minutes before serving.

Keep the finished cookies in an airtight container at room temperature for up to four days. To prevent sticking, layer the cookies between sheets of wax paper.