From the Super Mario Wiki
Peasley's Rose is an item found in Mario & Luigi: Superstar Saga. Mario and Luigi climb Hoohoo Mountain and battle Dragohoho, who is really a transformed Prince Peasley under Cackletta and Fawful's spell. The prince rewards them with the Peasley's Rose. The white rose is autographed and used as a pass to Beanbean Castle. It proves that Mario and Luigi are friends of the prince and the guards allow them to enter.