In a medium bowl, cream together the butter, white sugar, and confectioners' sugar until light and fluffy. Mix in the lavender, mint, and lemon zest. Combine the flour, cornstarch, and salt; mix into the batter until well blended. Divide dough into two balls, wrap in plastic wrap, and flatten to about 1-inch thick. Refrigerate until firm, about 1 hour.

Preheat the oven to 325°F (165°C). On a lightly floured surface, roll the dough out to 1/4 inch thickness. Cut into shapes with cookie cutters. Cookie stamps will work well on these too. Place on cookie sheets.