In a large bowl, cream together the softened butter and granulated sugar until light and fluffy.

Beat in the vanilla extract, lemon zest, and finely ground lavender buds.

In a separate bowl, whisk together the flour and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.

Shape the dough into a disc, wrap in plastic wrap, and chill in the refrigerator for at least 30 minutes.

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

Roll out the chilled dough on a lightly floured surface to about 1/4-inch thickness. Cut out cookies using your desired cookie cutters.

Place the cookies on the prepared baking sheets and bake for 10-12 minutes, or until the edges are lightly golden.

Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.

For the glaze: Whisk together powdered sugar and 1 tablespoon of lemon juice. Add more lemon juice, a teaspoon at a time, until desired consistency is reached. Drizzle over cooled cookies and sprinkle with extra lavender buds if desired.