The famed chef and handbag designer Gelila Assefa are having their second son

Celebrity chef Wolfgang Puck and his fiancée, handbag designer Gelila Assefa, are expecting their second child, his rep tells PEOPLE.

The baby boy, due in December, will be the second son for Puck, 57, and Assefa, 37. The couple’s first child, Oliver, was born in July 2005.

Puck also has two sons from his first marriage, to business partner Barbara Lazaroff.

The Austria-born Puck, who owns the new Beverly Hills steakhouse Cut at the Beverly Wilshire hotel and several upscale California eateries, has restaurants around the world, including ones in several major airports. His line of kitchen products and cookware is sold on the Home Shopping Network.