Tony and Mushtaq86, thanks for the input.
After looking through all the photos in the gallery labelled "ice cream" (including some of yours), I can see why you would say ice cream. But I think you are both wrong (and perhaps many of the plants that have been sold as ice cream are in fact something else).
Here's my logic:
1) Ice cream fruits, especially when young, are very bluish. My neighbor's bananas are not.
2) Ice cream (Ney Mannan subgroup) fruits have thick peels (3 mm or thicker, according to the MGIS database). These bananas have very thin peels (1-2 mm).
3) Ice cream fruits are not noted to have any apple flavor -- my neighbors bananas have a very strong apple flavor.
Here are some photos of real ice cream banana plants that I took at Quail Gardens in San Diego (Encinitas), California.
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And here's one from one of our "resident" experts, Gabe:
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I think my neighbor's bananas are probably some Pisang Awak (Namwah) cultivar, based on what I can tell and some of Gabe's comments.