Fresh off the tree, a quince is covered in fuzz that needs to be removed before you can peel the fruit. Commercially, quince is gently rubbed with brushes to remove the fuzz; in the home kitchen, I gently rub the fuzz off under running water, washing the fruit simultaneously.
Because the fruit is irregularly shaped, squaring it will make peeling and cutting easier. With a sharp knife, cut off the top and the bottom of the quince, close to the stem. Don’t worry about salvaging every bit of usable fruit. (But if thrift is in your nature, cover the discarded flesh, peels, and cores with lemon water and use them as a base for jelly.) You can also harvest and dry the seeds for medicinal purposes.
Unlike an apple, a quince is too bumpy, lumpy, and valleyed to peel in a circular motion. You’ll get best results from using a broad-bladed potato peeler instead of a thin vegetable peeler. Starting from the stem-side top (generally smaller in diameter than the base), remove the peel by making confident downward strokes, working around the fruit’s circumference. After peeling, check and remove all blemishes. Quinces bruise easily, which is why commercially grown quinces are picked and packed by hand.
You are now ready to quarter and core the fruit. Again unlike apples, quince cores tend to be irregularly shaped and off center, so an apple corer won’t do the job. You will need to cut. Select a sturdy, sharp knife (I like a fruit knife), set the blemish-free, peeled fruit top-side up on a cutting surface, and quarter the fruit, with an eye to cutting around the core once you locate it. Note that it is easier to cut around the core than through it!
Once you have quartered the quince, completely remove its core with a sharp melon baller, paring knife, or peach pitter. A peach pitter is the most unusual tool in the quince kitchen, but the most useful. It’s a must have if for both the quince and Armenian kitchens.