Prepare for baking: Preheat your oven to 350°F (180°C / gas mark 4). Line two baking sheets with parchment paper.
Combine dry ingredients: In a small bowl, whisk together the flour, cornstarch, and baking powder. Set aside.
Beat butter and sugar: In a large mixing bowl, cream together the butter, granulated sugar, lemon zest, and lavender buds using a stand mixer fitted with a paddle attachment (or electric mixer) on medium speed. Beat until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Add egg: Mix in the egg until well combined.
Incorporate dry ingredients: With the mixer on low speed, add the flour mixture, blending just until combined. The dough may seem slightly dry, but that’s okay.
Scoop cookies: Using a small cookie scoop, drop 1-tablespoon-sized balls of dough onto the prepared baking sheets. Leave about 2 inches (5 cm) between each cookie.
Flatten cookies: Gently flatten each dough ball with your palms until they are about 1/3 inch (1 cm) thick.
Bake: Bake the cookies for 12-15 minutes, or until the centers are just set and the edges are slightly golden. Bake one sheet at a time for best results.
Cool: Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.
Mix glaze: In a medium bowl, whisk together the powdered sugar, lemon juice, and lavender extract (if using). The glaze should be thick but pourable. Add a few drops of purple food coloring for a beautiful hue.
Decorate cookies: Spoon the glaze over each cooled cookie. Optionally, garnish with lavender buds and lemon zest for an extra touch of flavor and decoration. Let the glaze set for 30 minutes before serving. Enjoy!