Preheat oven to 350 F. Line baking sheets with parchment paper.

In a small bowl, combine flour, baking powder, and salt.

In a medium bowl, combine sugar and lemon zest. Rub together until fragrant.

Add butter to lemon sugar mixture and beat until light and fluffy. Beat in egg and vanilla until smooth. Mix in violet syrup, adding more if a strong violet flavor is desired.

On low speed, beat in flour mixture until combined. Add small drops of red and blue gel food coloring, mixing together until dough is the desired shade of purple.

Drop dough by the tablespoon onto prepared baking sheets. Gently flatten each drop of dough with the palm of your hand.

Bake 12-14 minutes or until cookies are just set and slightly golden brown around the bottom. Cool on baking sheet for 2 minutes before transferring to wire rack to cool completely.

Whisk together powdered sugar, violet syrup, and lemon juice. Taste and adjust as needed.

Add small drops of red and blue gel food coloring, mixing together until glaze is the desired shade of purple.

Dip cookies into the glaze and let set.