In a shallow dish combine sugar and cardamom. Wet rim of a chilled cocktail glass with water; dip in sugar mixture to coat. In a cocktail shaker combine cognac or Armagnac, Cardamom-Clementine Syrup, and lemon juice. Fill with ice. Cover and shake to chill. Strain into prepared glass.
Using a vegetable peeler, cut peel from clementines or orange, avoiding the white pith. (Reserve fruit for another use.)
In a small saucepan combine peel, sugar, water, and green cardamom pods. Bring to boiling; reduce heat. Simmer mixture until sugar dissolves, stirring constantly. Cool the syrup; transfer to a bowl.
Cover and chill for 2 days. Remove cardamom and peel. (Peel can be used for garnish.)