Wash the quince well to remove any fuzz. Cut each quince in half. Carefully remove the core and any tough bits, like the stem. Cut each half in half, to make quarters.
While you're preparing the quince, combine the sugar and water in a large saucepot. Bring to a boil, then add lemon peel, vanilla bean, and allspice berries.
Add the quince quarters to the hot syrup. Cut out a round piece of parchment paper to place on top of the quince as they simmer. This helps keep them submerged under the syrup.
Turn the heat down to a low simmer and let the quince cook until easily pierced with a knife. I've seen sources that say this can take an hour or two, but mine were plenty soft in about 35 minutes, so keep an eye on them. Time may vary depending on type of quince and how ripe they are.
Once the quince are soft, turn off the heat and let them come to room temperature in the syrup.