Preheat the oven to 350°F. Wash, halve, and core:

Rub generously with:

Place in a baking dish, cover, and bake until just tender when pierced with a knife. Check after 1 hour and if the flesh is still very firm, continue baking and checking for up to 1 more hour. Remove from the oven (but leave the oven on). Scoop out most of the flesh, reserving the rinds for presentation. Mix the flesh with:

Stuff the quince shells with the mixture. Return to the oven and bake until tender, about 15 minutes more. Serve hot or chilled.