In the bowl of a stand mixer, cream together butter and sugar. Add vanilla and beat to combine.
In a separate bowl, combine flour, cornstarch, and salt. Add the flour/cornstarch mixture to the butter/sugar mixture a third at a time, mixing after each addition. Add lavender with the final third of flour mixture. Dough will be crumbly.
Spread a teaspoon of flour on work surface. Turn out dough and work into a ball. Rub surface with flour. Roll into 1-inch log, wrap tightly with plastic wrap and chill for 30 minutes.
Preheat oven to 350º. Line a cookie sheet with parchment paper or a silicone mat. On a very lightly floured surface, roll dough out to ¼” thick. Cut cookies with a 3" round cutter. Poke holes in cookies with a fork. These cookies will not spread while baking, so they can be placed close together on the cookie sheet.
Bake 18-20 minutes. Color will stay light, but dough will be set. Cool 10 minutes. Makes 20-24 3-inch cookies.