01 - Using a stand mixer or hand mixer, beat the softened butter and powdered sugar on medium-high 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 creamed mixture. Continue mixing until fully distributed and the lavender is evenly throughout the dough.
03 - Reduce mixer speed to low and gradually add the flour, mixing just until the dough comes together and no dry streaks remain. Avoid overmixing to maintain tender texture.
04 - Divide the dough into two equal portions. Roll each portion into a uniform log approximately 2 inches in diameter. Wrap tightly in plastic wrap and refrigerate for a minimum of 30 minutes until firm.
05 - Preheat oven to 350°F. Line two rimmed baking sheets with parchment paper for easy cleanup.
06 - Remove chilled dough logs from refrigerator. Using a sharp knife, slice into 1/4-inch thick rounds. Arrange cookies on prepared baking sheets, leaving 1 inch of space between each cookie.
07 - Bake for 14 to 16 minutes, rotating pans halfway through, until edges are lightly golden and centers are set. Cool on baking sheets for 5 minutes before transferring to wire rack.
08 - Whisk together powdered sugar, 2 tablespoons lemon juice, and lemon zest in a small bowl until smooth and glossy. Adjust consistency with additional lemon juice if too thick.
09 - Drizzle or spread the glaze over completely cooled cookies. Sprinkle with additional lavender buds if desired. Allow glaze to set for at least 30 minutes before serving or storing.