1. Combine 1/2 cup water and cardamom in a small, heavy saucepan; bring to a boil. Remove from heat; cover and let stand 20 minutes. Strain through a fine sieve over a small bowl; discard solids.
2. Combine 1 tablespoon cardamom water and sugar in pan over medium heat, and cook for 9 minutes or until sugar is melted and barely golden (do not stir). Increase heat to medium-high, and cook for 1 minute or until mixture darkens to a deep amber. Remove from heat; carefully pour remaining cardamom water down the side of the pan. Return pan to medium-high heat; stir until well blended. Remove pan from heat.
3. Peel oranges. Cut each orange crosswise into 6 slices. Arrange slices on a rimmed platter; pour hot syrup over oranges. Cover and chill overnight.
4. Combine yogurt, honey, and orange-flower water in a small bowl. Serve yogurt mixture with oranges. Garnish with mint sprigs, if desired.