Cream together unsalted butter and granulated sugar in a large mixing bowl using an electric mixer on medium speed for about 3-5 minutes until light and fluffy.

Gradually add all-purpose flour, lemon zest, and dried culinary lavender to the butter-sugar mixture on low speed. Fold in the egg until the dough is smooth.

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

Preheat your oven to 350°F (175°C). Roll out the chilled dough to approximately ¼ inch thick and cut out desired shapes.

Place the cookies on a parchment-lined baking sheet and bake for 10-12 minutes until the edges are slightly golden brown.

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

Prepare the icing by whisking together powdered sugar, lemon juice, and milk until smooth and pourable.

Once the cookies are cool, dip the tops in icing or drizzle over them and sprinkle with dried culinary lavender.