This is a bathroom sink that is heavily overused for bathing various parts of Indian peoples' bodies.
This term originates from the annals of the financial world, where all people who work for SocGen (Societe Generale) seem to be Indians that are outsourced. Therefore, in this usage, SoGenese simply refers to people of an Indian heritage or descent. A bathroom sink where large numbers of them constantly wash their faces, arms, and heads is referred to as a SocGenese Birdbath.
When I walked in the bathroom to take a leak, it was like a freaking SocGenese Birdbath in there.