In a large mixing bowl, cream together the butter, sugar, lavender, mint, thyme and lemon zest with an electric hand mixer for three minutes or until light and fluffy.
Sift together flour, cornstarch and salt and combine with the butter mixture. Beat until well incorporated.
Divide the cookie dough in half. Flatten into squares and wrap in plastic wrap. Chill until firm.
Preheat an oven to 325°F/160°C. Line two cookie sheets with parchment paper.
On a floured board, roll or pat out each square to 1/2-in. thick. Cut the dough into 1 1/2-in. squares or rounds.
Transfer the cut shapes to cookie sheets, spacing the cookies about one inch apart. Prick each cookie several times with a fork.
Bake for 20 - 25 minutes, until pale golden color (do not brown). Cool slightly, then transfer to a rack.
Sprinkle with lavender sugar.