Preheat oven to 325° F.
Cover bottoms of two baking sheets with parchment or brown paper. In a large bowl, cream together the butter, sugar, lavender, and mint with an electric mixer. Mix until light and fluffy, about 3 minutes. Add flour, cornstarch, and salt and beat until incorporated. Divide dough in half. Flatten into squares and wrap in plastic. Chill until firm.
On a floured board, roll or pat out each square to a thickness of 1/2 inch. Cut the dough into 1 1/2 inch squares or rounds. Transfer to baking sheets, spacing cookies about 1 inch apart. Prick each cookie several times with a fork. Bake 20 to 25 minutes until pale golden (do not brown). Cool slightly, then transfer to a rack. Sprinkle with lavender powdered sugar.
Garnish with lavender powdered sugar: Put a 4 or 5 sprigs of lavender flowers in a sealed jar with powdered sugar for a day before using the sugar.
Makes about 4 dozen
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