Bowls of this unique, elegant form come from the islands of Wuvulu and Aua, in the Bismarck Archipelago (Papua New Guinea). The culture of these two islands is actually Micronesian rather than Melanesian, and the minimalist feel of these bowls is typical of the Micronesian aesthetic. Although an early visitor reported seeing them used to serve fish, bowls like this one are mainly used to collect coconut milk. Grated coconut meat is squeezed over the bowl, and the liquid runs down into the deep center.
For another example of elegant Micronesia carving, with a related function, see the Nukuoro Coconut Grater Stool, Object of the Day # 27
Penn Museum Object #P3482B
See this and other objects like it on Penn Museum’s Online Collection Database