You won’t see this mission before Chapter 08. Make sure you also trigger the “A Brave New World” main quest. An introduction cutscene will come up called “A Need for Noodles.
Gladio will ask you about your favorite ingredient, triggering a quest path with each answer.
You will be given three scenarios, each depending on which ingredient you chose:
Reach the designated area just south of Prairie Outpost in Leide. Kill Behemoth, and then make camp at a nearby haven. Choose cup noodles. Equip your best greatsword and shield! Focus on defending and parrying to make every counterattack possibility count. One strategy is to target its legs to topple the creature so you could quickly deal a ton of damage.
Go to the top of Rock of Ravatogh in Cleigne. Head right through a small path until you see the giant nest. Interact with the eggs in the nest. After that, leave the area by going through the tunnel on the other side. You should rest at a haven to complete the assignment.
This scenario requires you to go to Cape Caem in Cleigne. Follow the waypoint, which leads you slightly westward. You’ll have to fight a Karlabos. This beast is weak to Swords, Polearms, and Ice, but is resistant to fire damage. Ignis’ Enhancement technique is useful here.