A Hamelin researcher is beside himself with worry, as he lacks the materials needed to make medicine for his ailing sister.
This errand is available after completing Errand 010.
Talk to the man near the black market in Hamelin and agree to help him find the missing ingredient for the medicine he's making. Check your inventory to see if you have any Carrot Cakes left (one will suffice). If not, create one through alchemy by using a Cake + Crunchy Carrot x3 (and if you don't have those ingredients either, buy them from the Hootique).
With a Carrot Cake in your possession, head to the forest on the far west side of the continent and enter the hidden forest glade. Talk to the single lady and swap the cake for a feel-good fungus. Then return to the man to complete the errand.