01 - Place softened butter and powdered sugar in a large mixing bowl. Beat with an electric mixer on medium-high speed until the mixture becomes pale yellow, light, and fluffy, approximately 3 to 4 minutes. Scrape down the bowl sides halfway through to ensure even incorporation.
02 - Add the grated lemon zest, chopped lavender, and salt to the creamed butter mixture. Mix on low speed for 1 minute until fully distributed and fragrant. Scrape the bowl again to combine any ingredients stuck to the sides.
03 - Gradually pour in the all-purpose flour while mixing on the lowest speed. Continue mixing just until the dough forms a cohesive ball and no dry flour streaks remain visible. Avoid overmixing to prevent tough cookies.
04 - Divide the dough into two equal portions. On a clean surface, roll each portion into a log approximately 2 inches in diameter. Wrap each log tightly in plastic wrap and refrigerate for at least 30 minutes or up to 24 hours until completely firm.
05 - Preheat the oven to 350°F. Line two large baking sheets with parchment paper, leaving slight overhang on the sides for easy removal.
06 - Remove one dough log from the refrigerator. Using a sharp knife, slice into rounds approximately 1/4 inch thick. Place the slices on the prepared baking sheets, spacing them 1 inch apart to allow for minimal spreading. Repeat with the second log.
07 - Bake one sheet at a time on the center oven rack for 14 to 16 minutes. The cookies are done when the edges are just beginning to turn light golden brown while the centers remain pale.
08 - Let the cookies rest on the baking sheets for 5 minutes to firm slightly. Carefully transfer to a wire cooling rack and allow to cool completely to room temperature before icing, approximately 30 minutes.
09 - In a medium bowl, whisk together the powdered sugar, 2 tablespoons lemon juice, and lemon zest until completely smooth and glossy. The glaze should have a thick but pourable consistency. Add additional lemon juice 1 teaspoon at a time if too thick.
10 - Drizzle or spread a small amount of lemon glaze over each cooled cookie using a spoon or offset spatula. Immediately sprinkle with a few lavender buds if desired. Allow the glaze to set for at least 20 minutes before serving or storing.