Preheat oven to 350°F (180°C) and line 2 baking sheets with parchment paper.
In a small bowl, whisk together flour, baking powder, and cornstarch. Set aside.
In a large bowl, beat butter, sugar, lemon zest, and lavender until light and fluffy (2–3 min).
Mix in the egg until fully incorporated.
Gradually add the dry ingredients on low speed until dough comes together.
Scoop 1 tbsp of dough, place on baking sheet, and gently flatten to ⅓ inch thick.
Bake for 12–15 minutes until edges are just golden.
Cool 5 minutes on tray, then transfer to a wire rack.
Mix glaze ingredients until smooth. Glaze cooled cookies and top with zest or buds.
Let glaze set for 30 minutes before serving or storing.
