Put the quinces in a heavy-based pot with the cardamom and add about 1/2 inch of water to prevent burning.
Cook, covered, for about 1 hour, keep checking that the water hasn't disappeared.
When the quinces are soft (but not falling apart). add the sugar and stir until dissolved
Let the mixture cool, then stir in the cointreau
Let the mixture cool, then stir in the Cointreau