"Caro mio ben" is a standard from the beginning singer's 24 Italian Songs and Arias. It is attributed to Giuseppe Giordani (1744-1798). Here is mezzo Cecilia Bartoli singing her rendition in June 1998 with Jean Yves Thibaudet on piano.
This version is by tenor Luciano Pavarotti from a 1978 recital with John Wustman accompanying.
Mutopia Project.org has a link to a .pdf file of the sheet music for "Caro mio ben" in the key of D as well as a midi file.
See also Art Song Central.