Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
In a large mixing bowl, cream the softened butter and granulated sugar until light and fluffy.
Gradually mix in the flour, lemon zest, and dried culinary lavender until just combined.
Add the egg and mix on low speed until incorporated. Avoid overmixing to keep the cookies tender.
Form the dough into a disc, wrap it tightly, and refrigerate for at least 30 minutes.
Roll the chilled dough to approximately ¼-inch thickness.
Cut into your favorite cookie shapes using cookie cutters.
Arrange the cookies on the prepared baking sheets.
Bake for 10–12 minutes until the edges are lightly golden.
Cool completely on a wire rack.
Whisk together the powdered sugar, lemon juice, and enough milk to create a smooth glaze.
Spoon or drizzle the icing over each cookie. Allow the icing to set completely before serving.
These Iced Lemon Lavender Shortbread Cookies taste even better after the glaze has fully hardened.