You've traveled to all sorts of familiar places in The Legend of Zelda: Tears of the Kingdom. Upon arriving at Kakariko Village, you'll learn of the hardships the locals are experiencing. After helping the nearby grocery shop once already, things are looking up.
But all is not well. Trissa now explains that there is a shortage of eggs, but the local Cuccos have been running off every morning, so she can't get the eggs she needs.
This quest is not available until after you complete the Codger's Quarrel side quest.
How To Start And Complete The Follow The Cuccoos Side Quest
Go to Kakariko Village and visit the grocery store near the entrance. You can begin the quest as soon as you complete the Codger's Quarrel side quest.
Completing the quest is as simple as giving Trissa ten eggs. You do not need to find the cuccoo's hiding place, nor do you need to get those eggs specifically. Any ten eggs will do. Give her the eggs, and she will reward you with 50 rupees (slightly above market value had you sold eggs outright).
How To Find The Cuccoos Hiding Place In Kakariko Village
Trissa will remark that all of the cuccoos in town run off early in the morning, but she is too old and slow to keep up. You can follow them yourself to discover their secret hiding place.
All of the cuccos will leave Kakariko village at exactly 5 AM in-game. They run up the wooden ramps in town and head east up the mountain. They will gather at Cave up the mountain, on the northern side of the Pillars of Levia. Inside, you'll find multiple bird nests with eggs.
The cave can be explored further by breaking the destructible rock walls found throughout. This will lead to an encounter with a Likelike and a Bubbelfrog.
Collect the eggs and deliver them to Trissa. Or keep them. The location will resupply with eggs over time, so return whenever you need the ingredient.