Preheat oven to 375°. In a medium bowl, thoroughly blend sugar and orange zest, then blend in cardamom. Add butter and beat with a mixer until light and fluffy.
Beat egg and vanilla into sugar-butter mixture. On low speed, mix in flour.
Line 3 baking sheets with parchment paper. Drop batter onto sheets using a level teaspoon measure. Top each cookie with a pinch of sesame seeds or nuts if you like. Bake until crisp and brown at the edges, 10 to 12 minutes.
Transfer cookies to a cooling rack and let cool completely.