In a large saucepan, bring 3 cups water and remaining ingredients except quinces to a simmer over high heat. Add quinces, reduce heat, and simmer, uncovered, until quinces are tender when pierced, 30 to 35 minutes.
With a slotted spoon, transfer quinces to 3 widemouthed pint jars. Lift out cinnamon, bay, and star anise; cut into pieces with kitchen scissors; and return to liquid. Pour liquid over quinces, dividing spices; let cool. Chill, covered, at least 1 day before serving.
*Lay pieces on their sides on a work surface to cut out the firm cores.
Make ahead: Up to 1 week, chilled.