01 - In a large mixing bowl, beat the softened butter and powdered sugar together using an electric mixer on medium speed until the mixture becomes pale, light, and fluffy, approximately 3 to 4 minutes.
02 - Add the lemon zest, chopped lavender, and salt to the butter mixture. Mix on low speed until evenly distributed throughout the dough, scraping down the sides of the bowl as needed.
03 - Gradually add the all-purpose flour to the bowl, mixing on low speed just until the dough comes together and no dry flour streaks remain. Avoid overmixing to prevent tough cookies.
04 - Divide the dough into two equal portions. Shape each portion into a uniform log approximately 2 inches in diameter. Wrap each log tightly in plastic wrap and refrigerate for at least 30 minutes or until firm enough to slice cleanly.
05 - Preheat the oven to 350°F. Line two large baking sheets with parchment paper and set aside.
06 - Remove one chilled dough log from the refrigerator at a time. Using a sharp knife, slice the log into 1/4-inch thick rounds. Arrange the cookies on the prepared baking sheets, leaving about 1 inch of space between each cookie.
07 - Bake the cookies for 14 to 16 minutes, or until the edges are barely golden brown while the centers remain pale. Remove from the oven and let the cookies cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
08 - While the cookies cool, whisk together the sifted powdered sugar, lemon juice, and lemon zest in a small bowl until smooth and glossy. Adjust the consistency by adding more lemon juice if too thick or more powdered sugar if too thin.
09 - Drizzle or spread the lemon glaze over the completely cooled cookies. If desired, sprinkle a few whole lavender buds on top of the wet glaze for decoration. Allow the glaze to set for at least 15 minutes before serving or storing.