This is a quince. It looks like "karin", or Chinese quince, but it is slightly different. I used this size for this recipe (it was about 340 g after removing the seeds).
Since you will cook the skin also, rinse it well.
Remove the seeds, and cut into bite-sized pieces while soaking the cut pieces in a bowl of water to prevent it from discoloring.
Combine all of the ingredients in a pot and turn on the heat to low.
Bring it to a boil. When the flesh is tender and the quince becomes immersed in the juices, it is ready.
Pack it in a jar while still hot. If there is not enough liquid, add honey.
You can eat it as-is, or else it is delicious to drink it by diluting it with hot water or sake.
Story Behind this Recipe
When I was little, my grandmother always had a stock of this for us. I used to pretend that I had coughs, so that I could have some.
Caution! Since this is made with honey, do not feed it to a child under the age of 1.
It tastes great and has a crunchy texture if you soak the fresh quince in the honey, but it's better to make it into jam, so that you can store it. In Step 5, you can also mash the flesh. Whichever way you like.