I live in just outside of New York City and frequently go into the city for fun. 
I have lots of favorite places to go and places to eat. One of these is the Chinatown Ice Cream Factory at 65 Bayard Street. It is a bit of a trek to get there if you aren’t doing things in Chinatown or the surrounding neighborhoods, but it well worth the journey. It is a small shop that is always crowded, there is only a counter and enough space for people to come in and get their ice cream. You will always find a crowd outside, happily eating ice cream and enjoying the sights of Chinatown.
They make their own ice cream and have a marvelous assortment of flavors, some of which I have only seen there. I have tried quite a few and it is hard for me to pick a favorite because they are all so good. I have tried Lychee, Mango, Green Tea, Coconut, Ginger and Red Bean. Sometimes when I go with a bunch of friends we just buy a few pints and then grab spoons and feast.
I have never been disappointed with the ice cream and will go out of my way to stop there even in the middle of winter to get my special treat of their delicious ice cream.
The sign marks the spot!
Ginger, with real ginger pieces! mmmmm
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Two Different Girls 
It sounds delicious, plus they make it themselves! I would love mango, though like you I think I would like to grab an assortment with friends and taste them all.
ohmygawd. i live in nyc and will be going there asap.
Ooooo, ginger ice cream.