A subtropical fruit, Annona cherimola, that originated in the inter-andean valleys of South America, from whence it has spread as far north as California in the Americas and to Asia, Australia, and New Zealand. Today there are many varieties cultivated.
The fruits are about the size and shape of a medium artichoke and have three skin types: impressa (smooth or slightly indented); tuberculate (with raised protuberances); or intermediate (a combination). Cherimoya are a compound fruit or syncarpium, meaning that several pistils fuse together into a single mass along a central receptacle around which are arranged spiralled carpels or segments, kind of like a raspberry; each segment of flesh contains a single hard black seed. The flesh itself is meltingly smooth, custardy, and fragrant; it's a mix of sweet and acidic that causes connoisseurs to swoon as they scramble for descriptors: one source calls it cross between banana, passionfruit, papaya and pineapple. But Mark Twain cut to the chase in his inimitable fashion, referring to cherimoya as "deliciousness itself".
As subtropical trees, cherimoya require a cool season (though they will be killed by anything more than a very light frost); the trees are usually evergreen but can be briefly deciduous in some areas. The varieties grown in California are apparently difficult to pollinate because the male and female flowers do not mature at the same time; hand pollination is required to ensure that the pollen reaches the receptive ripe stigma. The seeds, by the way, are toxic, and can be ground and used as insecticide.
When buying cherimoya, choose firm, unripe fruit that are heavy for their size. Store them at room temperature and allow them to ripen naturally; they should give slightly to a gentle pressure, but not be squishy. Once they are slightly soft, like an almost-ripe avocado, let them sit for another day, then eat or store in the fridge for a few days. To eat, cut in half and eat out of hand or with a spoon. Or pull off the skin and eat whole or sliced. Spit out the seeds, of course; you'll have lots, as there can be dozens per fruit.
I have never attempted to do anything with cherimoya other than gobble them down as is, but apparently they make great ice cream, sherbet and dessert sauces.
Cherimoya are distantly related to, and sometimes confused with, pawpaw; a close cousin, considered by some to be inferior, is the custard apple.