Meena Vathyam sent in this photograph from Shanghaiist:
This one is very easy to solve. The sentence actually means:
huíxiāng chǎo bènjī dàn 茴香炒笨鸡蛋
("fried free range eggs with fennel")
The translator misparsed the last part as bèn jīdàn 笨 鸡蛋 ("stupid egg") instead of the intended bènjī dàn 笨鸡 蛋 ("eggs from free range chickens").
Bènjī 笨鸡 ("free range chicken") is a northeast topolectal word for what in Modern Standard Mandarin (MSM) is normally referred to as tǔjī 土鸡 (lit., "local / native chicken"). I've also heard this type of fowl referred to as cháijī 柴鸡 (lit., "firewood chicken"). In Shandong this type of poultry is called cǎojī 草鸡 (lit., "grass chicken").
The semantics of the epithet "stupid egg" were discussed at length in "Ma Ying-jeou and Xi Jinping: presidential language notes".
[Thanks to Cao Lin, Cheng Fangyi, and Rebecca Fu]