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 1inch thick. Refrigerate until firm, about 1hour.                                                               

Preheat the oven to 325 degrees F. On a lightly floured surface, roll the dough out to 1/4 inch thickness. Cut into shapes with cookie cutters. Place on cookie sheets.                                                                                                        

Bake for 18 to 20 minutes in the preheated oven, just until cookies begin to brown at the edges. Cool for a few minutes on the baking sheets then transfer to wire racks to cool completely.                                                                   

Dust with confectioner's sugar.