Rrerku

All the instructions I've read for cooking quince talk about how much of a pain it is to peel and quarter them before cooking them till they are soft.

Am I missing something, or could I cook them till soft and then cut and core them?

No, this should work.

But you need to get that precise point between too hard and too soft to cut. And during cooking the fruit will soften from the outside inwards: You might find yourself handling the fruit during cooking, so either you have to touch hot fruit or interrupt the cooking, let cool, peel, cook again....

If you are aiming for quince puree, just rub off the fuzz, cook the fruit and then push it through a food mill or sieve. You'll need a pretty large pot though, if you want to cook whole fruits vs. smaller pieces.

On the other hand, if you have a reasonable sharp and heavy chef's knife and a sharp paring knife, I suggest you try cutting a raw quince first. You might find it less difficult than it's often said.

With quince the tedious part is peeling, not cutting, because the skin is tough and quince fruit is strangely shaped with lots of difficult areas. Once you have them peeled quartering them is just 2 cuts, which is not time consuming. If you have peeled them you may as well cook them in pieces and make your life easier.

You won't save time cooking them whole, in fact it will take longer if you want a good result. Think about a roast versus a steak - it's the same meat but the steak has a much higher surface area in proportion to its weight so it cooks an order of magnitude faster than the roast does. The same principle applies to quince - quartering the fruit means more surface area and therefore much faster and more even cooking. If you put a whole quince in liquid and boil it the outer part will cook much faster than the inner part and you'd end up with a soggy outside and raw inside, so to cook a whole quince properly you'd need to use a low temperature for a long time.

One thing you could try to speed things up with less effort would be to quarter the quince without peeling it, then cook it and skin it afterwards. This works for potatoes, but I have never tried it with quince and I really don't know if it will work. If you try it and it does please let us know.

Answer to the question about skins on quince.
I regularly cook my quince by Washing the bloom off, quartering and chopping down the core section and cooking with skins on. It's easy to slip off the cooked skin- in fact if cooked too long it will start to peel back on its own.