Old Master Cannoli
The stone statue of Old Master Cannoli is located inside the Secret Woods, in the very top left corner.
The statue reads: "Old Master Cannoli... still searching for the sweetest taste...".
If you buy and grow a Rare Seed from the Traveling Cart (for 
600–1,000g) and then give the statue the resulting Sweet Gem Berry as you would give a present, the statue's eyes will turn red and it will give you a Stardrop. This will only work one single time. After that, you won't be able to interact with it anymore.
Trivia
- Old Master Cannoli may be a reference to "Obi-Wan Kenobi" from the Star Wars Series, as the two share similar appearances, and their names even sound similar.