The Underground Misty Cave is located underneath Derkarr's Misty Cave. It leads back to the Misty Cave on the upper right by climbing up the rope, to the Ice Cave to the lower right side of the map, and to Spring of Revgato - Root to the far left.
The Underground Misty Cave, and the latter two areas connected to it, are not accessible for most of Chapter 1. To gain access to it, you need to finish "The Missing Rabbit" event in Chapter 1.
There are no ingredients or common enemies found in this area. There are, however, two event battles here in the "Underground Misty Cave" event in Chapter 1.
Approach the area with light particles floating up. There is now a rope that leads further into the cave. Descend the rope. After viewing the tutorial about Teleportation Magic Circles, proceed left. (Eirudy will refuse to access the Ice Cave for the time being, as she is more concerned about Adrian.)