After completing The Gourmet Supremos: The Deep Divers world quest, head on over to Inazuma City to find Xudong, Julie, and Parvaneh. They'll be located right near the Adventurer's Guild desk with Katheryne.
This time, instead of retrieving a certain ingredient for the Gourmet Supremos, you'll be accompanying them on their journey through Chinju Forest. This is a straightforward quest that involves no combat or puzzles.
Venture into the forest and speak with the mysterious samurai, then interact with the three highlighted areas to collect ingredients. Afterwards, you'll be prompted to find a good spot for cooking.
Completion of The Gourmet Supremos: On the Road counts towards your Inazuma reputation, which you can check at the Kamisato Estate on Narukami Island. In addition, you'll also receive the following quest completion rewards:
- Adventure EXP (100)
- Mora (10,000)
- Hero's Wit books (3)
- Delicious Jewelry Soup (3)
The next quest in the series is Gourmet Supremos: Breakthrough Thinking, which is a daily commission quest. After completing this commission at least once, The Gourmet Supremos: The Importance of Eating Well will become available to undertake in Inazuma City.