Wash and peel the quinces. Place in a container of water with a splash of vinegar to prevent discoloration. Grate the quinces. Remove the quince seeds from the core and place in a cheesecloth. Tie the cheesecloth in a knot so the seeds are held inside (the seeds have some natural pectin, which will help form the paste).

Transfer the quinces to a pot (preferably copper), cover with 3 cups water, add ½ cup sugar and the wrapped quince seeds, and bring to a boil. Reduce heat, cover, and simmer over low heat for about 2 hours or until tender, stirring occasionally with a wooden spoon.

Squeeze and then remove the wrapped quince seeds from the pot and discard. Use a food processor to puree the quinces. Return to the pot, and add remaining sugar, lime juice, cardamom, and rose water. Cover and simmer over medium-low heat for 4 hours or until you have a thick reddish paste, stirring occasionally with a wooden spoon. Uncover and cook for another hour. Transfer to an oiled (or lined with parchment paper), rimmed quarter-size sheet pan, or mold. Garnish with pistachios. Leave uncovered at room temperature overnight, or longer, until firm.