Blend sugar, lemon zest, and lavender in a food processor.
Cream butter with lavender sugar until light.
Add egg, lemon juice, and vanilla; mix.
Gradually add dry ingredients; form dough.
Chill dough for 2 hours.
Roll into balls, flatten, and bake at 350°F for 10–12 minutes.
Mix glaze ingredients and drizzle over cooled cookies.
Notes
- Chill dough to maintain shape. - Adjust lavender to taste if stronger or milder floral notes are desired. - Cookies can be frozen (unbaked or baked without glaze).