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

Add the lemon zest and finely crushed culinary lavender to the butter mixture. Beat until well combined, scraping down the sides of the bowl as needed.

In a separate bowl, whisk together the all-purpose flour and salt.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and a soft dough forms. Be careful not to overmix.

Divide the dough in half. Shape each half into a log, about 1.5 inches in diameter. Wrap each log tightly in plastic wrap and refrigerate for at least 30 minutes, or up to 2 hours, to allow the butter to firm up and the flavors to meld.

Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper.

Remove one dough log from the refrigerator. Using a sharp knife, slice the dough into 1/4-inch thick rounds. Place the cookies about 1 inch apart on the prepared baking sheets.

Bake for 12-15 minutes, or until the edges are lightly golden and the centers are set. The cookies should still be pale. Do not overbake.

Let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. Repeat with the second dough log.

While the cookies cool, prepare the lemon glaze. In a small mixing bowl, whisk together the powdered sugar and fresh lemon juice until smooth. Add more lemon juice a teaspoon at a time if the glaze is too thick, or more powdered sugar if it's too thin, until you reach a drizzling consistency.

Once the cookies are completely cool, drizzle the lemon glaze over them using a spoon or a small whisk. If desired, sprinkle a pinch of finely crushed culinary lavender on top of the wet glaze for an extra touch.

Allow the glaze to set for about 15-20 minutes before serving or storing.