Preheat oven to 375°F. Line a cookie sheet with parchment paper or a silicone baking mat.
In a stand mixer fitted with a paddle attachment cream together the butter and both sugars until lightly and fluffy. Add in the vanilla extract. Add in the eggs, one at a time and mix thoroughly scraping down the sides every so often.
In a small bowl combine the flour, lavender buds, baking powder, salt and baking soda. Add to the butter mixture and combine until you no longer see any flour.
Using a small to medium sized ice cream scoop or large spoon, drop the cookies onto the cookie sheet. Do not press down. Bake for 9-11 minutes until golden brown and set. The bottom will get darker than the tops. Remove and let cool on a cooling rack. Continue with remaining dough. Makes 24 cookies.
In a small bowl combine the powdered sugar and milk. Whisk until smooth. Once cooled, frost the cookies and sprinkle with some of the lavender buds. Will keep in an airtight container for 3-4 days.