In a food processor, pulse the granulated sugar and dried culinary lavender until the lavender is finely ground and fragrant.

In a large bowl, cream the softened butter and the lavender sugar until pale and fluffy (about 3 minutes).

Beat in the egg, vanilla extract, lemon zest, and lemon juice until combined.

Whisk together flour, cornstarch, baking powder, and salt. Gradually add to the wet ingredients, mixing just until a dough forms.

Cover the dough and chill in the refrigerator for at least 1 hour.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Scoop dough into 1.5-inch balls and space 2 inches apart on the baking sheets. Flatten slightly.

Bake for 10-12 minutes until bottoms are lightly golden but tops remain soft and pale. Cool completely.

Whisk together powdered sugar, 2 tablespoons lemon juice, milk, vanilla, and food coloring. Add more lemon juice if too thick.

Spoon the glossy icing over the cooled cookies. Immediately garnish with fresh lavender buds and lemon zest before the icing sets.