SEOUL—After wolfing down four orders of fried chicken, Lee Dong-hyun stared at what remained on his plate: a puddle of curry sauce and some french fries. So he dumped in a bowl of rice to vacuum up what remained.

“The texture is so soft,” said Mr. Lee, 29, a muscular, binge-eating YouTube celebrity who goes by the moniker MBro, as he rhapsodized about the flavors for his nearly one million subscribers.

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