faucet handle broke off
You will need to buy parts that fit that exact faucet brand and model. You might be able to get them through the store where the faucet was originally purchased, or from the original installer.

OR you can try to contact the manufacturer yourself, they are a european (Italian, I believe) company: 
Ponsi
Phone: +39 030 6818511
Fax: +39 030 6818535
E-mail: info@ponsi.it