Put the quinces, 1/4 cup sugar, and 1 cup water in a heavy medium saucepan. Bring to a boil, reduce the heat, and simmer, covered, stirring occasionally, until the quinces turn pink and are beginning to soften, about an hour.
Add the apples, cinnamon stick, vanilla bean, and star anise to the pan and continue simmering, covered and stirring occasionally, for another 45 minutes, or until all the fruit is very tender. Taste for sweetness and add a bit more sugar if needed.
Remove from the heat and let cool, then fish out the spices and discard. Mash with a potato masher or put through a food mill using a medium disk. Serve slightly warm or cold.