This is a chayote, in the Philippines we call it sayote. It's a vegetable that's related to zucchini and cucumber, most commonly used in salads and stir fries. It has only about 39 calories per cup, nearly fat free, high in fiber and folate.
Chayote has almost no flavor of it's own, so it has to be paired with something to give it flavor. It is similar in texture with apples and there is even a rumor that McDonald's used them as an extender in their apple pies. I have tried making an "apple" pie using chayote, and yes, you can't really tell the difference except maybe the lack of apple flavor.
But did you know that you can also substitute apples with chayote in making apple sauce? Chayote, like apple, is also rich in pectin. Pectin, as we know, is an insoluble fiber that's a gelling agent in jams and jellies. In vegan baking, we use applesauce to replace fats because it is a good source of pectin. Pectin, in place of oil, prevents gluten formation in flour to make cakes light and fluffy. Click here for further reading.
Since chayote has almost no flavor, there won't be any distinct taste when used in baking, unlike applesauce which gives you a distinct apple taste. It's also a lot cheaper.
HOW TO MAKE CHAYOTE "APPLE SAUCE"
Peel and chop the chayote into small pieces.
You'll notice some little hairy filaments. We'll remove that by seiving it later.
Pop it in a food processor and blend until it turns into a mushy pulp.
This would be the raw "apple" sauce. I don't know what difference it makes when using raw or cooked applesauce in baking. If you want to use it raw, just sieve this and store in a jar.
For cooked applesauce, put it in a saucepan over medium heat. Cover and stir occassionally for 30-45 mins.
I just used 1 cup, without any water, so I stopped at 15 mins because it was already getting dry.
Raw vs cooked applesauce. The main difference would be the water content, I guess. The water would evaporate during cooking.
Raw and cooked apple sauce