Begin by creaming the butter and granulated sugar in a mixing bowl with a hand mixer on medium speed for about 3-5 minutes until light and fluffy.

Gradually mix in the all-purpose flour, lemon zest, and dried lavender until just combined; fold in the egg until the dough is smooth.

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

Preheat the oven to 350°F (175°C). Roll out the chilled dough to about ¼ inch thick and cut shapes with cookie cutters.

Bake the cookies on parchment-lined baking sheets for 10-12 minutes or until edges are lightly golden.

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

In a mixing bowl, whisk together powdered sugar, lemon juice, and milk or cream to achieve a smooth icing consistency.

Once cookies are cool, dip them into the icing or drizzle it on top. Optional: sprinkle dried lavender on top before the icing sets.