The Supply Run quest is given by Yomogi the Chef. She will ask you to retrieve the packages she lost that contain Fabled Spice.
How To Complete the Supply Run Request
Once you’ve accepted this quest from Yomogi the Chef, it’ll appear in the list of 3☆ Village Quests. This request is set in Shrine Ruins, and you’ll need to collect 6 Fabled Spice, which can be found in small packages scattered across the map. You can use your mini map to help you locate the packages.
Once you have collected all the Fabled Spices, return to Yomogi the Chef. After you’ve completed this request and reached 4☆ Village Quests, Yomogi will give you a second quest, Getting Back the Groceries.