Wrap quince peels and cores in cheesecloth and tie to secure well. In a saucepan combine bundle of peels along with quinces, sugar and water and cook over medium heat until mixture comes to a simmer. Reduce heat to low and continue to cook until quinces are very soft, about 1 1/2 hours. Remove from heat.

Preheat oven to 175 degrees. Discard cheesecloth bundle and transfer cooked quinces to the bowl of a food processor and process until smooth. Transfer mixture to a small baking dish or loaf pan and dry paste in the oven for 15 hours. (This drying procedure can be spread over several days.)