It was delicious fried tofu! You need a Rust-Worn Key to open it.
Once you finish the puzzle, you will have to battle against a Mysterious Samurai with fire-related attacks and rapid, sudden moves.
Head to the Grand Narukami Shrine.
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The Mysterious Samurai that you have to fight near the end of the quest, however, is not immune to any element and can be defeated with a well-rounded party.