Jay knows this fruit as sapodilla.  It was originally from here but is now found around the world in the tropics.  The Spanish and to a greater extent the Portuguese Empire had tropical ports and did a great deal in spreading exotic plants around the world.  In Mexico, these are often called chicoo although the scientific name is manilkara zapota. 
The one we ate yesterday tasted like a custardy, sweet pumpkin.   Jay had a bit of a stomach upset today and it's a toss-up whether it was the fruit or KFC.  There's a Kentucky Fried Chicken on this block and after about 30 years we got some take-away in a bucket.
