Zeff is the head chef at the Baratie' and although him and Sanji butt heads constantly, they care deeply for each other and have a very strong bond because of their history together. Zeff saved Sanji's life because he has the same dream as him that he was never able to achieve. He becomes the only father figure Sanji has ever had.

Sanji feels indebted to him and refuses to leave but Zeff forces him to go chase his dream. He was once a fearless pirate but because of Sanji he was forced to give up the life of a pirate and decided to start his own sea restaurant after but of them nearly starved to death stranded at sea.

Voice Reference @2:45 : https://www.youtube.com/watch?v=InktORJAlsA