POTSDAM, Germany — The official delegation honoring Frederick the Great’s 300th birthday had just finished laying a laurel wreath and a grand cross of white flowers at his grave here on Tuesday when a 70-year-old retiree quietly slipped in behind them and placed a small potato on the gray slab of stone that marks the monarch’s resting place.

“I’m a born Potsdamer and my father was, too, and I guess a little of the old Prussiandom is still in my veins,” said the man, Harry Günther, a retired engineer, standing before the yellow walls of Frederick’s magnificent summer palace, Sanssouci, on a chilly, foggy morning, a light coating of snow on the grass. He praised Frederick’s Prussian virtues, like hard work, honesty and thrift.

The potato, one of more than a dozen left by admirers, is a traditional token to honor Frederick’s role in spreading the cultivation of the food staple in his lands. “Old Fritz made sure they grew them,” Mr. Günther said, using the monarch’s popular nickname. “Plus, they last longer than flowers.”...