The Journey (2023)

Both are mini dramas in which a modern day cook travels back to ancient times and meets the ML.
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Both are mini dramas in which a modern day cook travels back to ancient times and meets the ML.
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Both are historical dramas with a fantasy/time travel twist about the ML and a FL who likes to cook.

Both have a historical setting, an emperor who is impossible to please with his meals, and a FL who is an excellent cook.