In a mixing bowl, cream together unsalted butter and granulated sugar until light and fluffy, about 3-5 minutes.

Gradually add all-purpose flour, fresh lemon zest, and dried culinary lavender to the mixture. Mix on low speed until just combined. Gently fold in the large egg.

Form the dough into a disc shape and wrap it tightly in plastic wrap. Refrigerate for at least 30 minutes.

Preheat your oven to 350°F (175°C). On a lightly floured surface, roll out the chilled dough to approximately ¼ inch thickness. Use cookie cutters to cut out desired shapes.

Bake the cookies for 10-12 minutes, or until the edges are golden brown.

Allow the cookies to cool on the baking sheet for about 5 minutes before transferring them to a wire rack.

In a separate bowl, whisk together powdered sugar, fresh lemon juice, and a splash of milk or cream until smooth.

Once the cookies have cooled, dip the tops into the prepared icing or drizzle it over each cookie. Sprinkle extra lavender buds on top before the icing sets.