Wash and remove fuzz from the quinces. Peel, core, and slice them, reserving the cores and peels.

Place the cores and peels into the center a large square of cheesecloth, then tightly tie the corners together to create a secure bundle. Put the slices in a large, heavy-bottomed pot, add water to cover the slices, and then add the bundle of scraps. (With the bundle added, my batch barely fit into a 4-quart Dutch oven; I’d recommend using an 8-quart pot for a recipe this size.)

Bring the pot to a boil over high heat, then bring the heat down to low and cook gently, uncovered, until the quince slices are very tender.

When the slices are falling-apart tender, remove and discard the bundle of scraps. Puree the quince and cooking water in the pot using an immersion blender until very smooth, with no lumps remaining. (If need be, you can do this in a few batches using a regular blender, then pour the puree back into the pot.)

Add the sugar and the rosemary to the pot and cook over low heat, stirring frequently, until the mixture turns a deep rosy pink and thickens to coat the back of a spoon. While you’re waiting, prepare a large water bath canner and enough half-pint or quarter-pint jars, bands, and lids for 6 pints of quince butter. For me, it took around 3 hours to get to the right stage; I removed the pot from the heat when the mixture was starting to firm up (not quite wrinkling when poked) when I did the plate test.

Ladle the quince butter into the hot jars, leaving ¼ inch headspace. Wipe rims, apply lids and rings, and process in a boiling water bath canner for 10 minutes. Allow the jars to cool undisturbed for 24 hours before checking seals, removing bands, labeling, and storing.