In a large mixing bowl, cream together the unsalted butter and granulated sugar until light and fluffy, about 2–3 minutes.

Add the lemon zest, lemon juice, and culinary lavender; mix until combined.

Gradually incorporate the all-purpose flour until just combined without overmixing.

Divide the dough into two equal portions, shape into discs, wrap in plastic wrap, and chill for at least 30 minutes.

Preheat the oven to 350°F (175°C) and roll out one dough disc to ¼ inch thick. Cut out shapes and place on a parchment-lined baking sheet.

Bake for 10–12 minutes or until edges are lightly golden. Let cool on baking sheet for 5 minutes before transferring to wire racks.

Whisk together powdered sugar and milk until smooth; adjust milk for desired consistency.

Glaze cookies after they are fully cooled, dipping or drizzling icing over cookies, then sprinkle with lavender.