Ingredients

• 1 3/4 lb quinces (2 large)
• 4 cups water
• 1 1/2 cups sugar
• 1 (12-oz) bag fresh or frozen cranberries (do not thaw; 3 1/2 cups)
• Special equipment: an 8-inch square of cheesecloth; kitchen string

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Instructions

1. Peel, quarter, and core quinces, reserving peel and cores, then cut quarters into 1/4-inch pieces. Tie up peel and cores in cheesecloth. Bring water and sugar to a boil in a 4-quart heavy saucepan, stirring until sugar is dissolved, then add quince and cheesecloth bundle and simmer, partially covered, until quince is tender, about 1 1/2 hours. Add cranberries and simmer, uncovered, stirring occasionally, until cranberries burst and soften, 8 to 10 minutes.
2. Drain mixture in a large medium-mesh sieve set over a bowl, discarding cheesecloth bundle and reserving cranberry solids, then return cooking liquid to pan and boil, uncovered, until syrupy and reduced to about 1 1/2 cups, 5 to 10 minutes. Stir together syrup and cranberry mixture in bowl, then cool to room temperature.