Place all syrup ingredients in a heavy-bottomed saucepan and bring to a boil. Reduce heat to medium and simmer for about 15 minutes until thickened and syrupy. Strain, and allow syrup to cool fully before use.
Pour 1 to 2 tablespoons of orange-cardamom syrup into each empty Champagne flute. Fill each glass with chilled Prosecco and serve.