Kill 8 snowy cliff beaks. These are birds found flying in air above the Goahmari Village and the hills surrounding it.
Click on the egg across from Norbu at ( 585, -37, 379 ) /waypoint 585, -37, 379. It can then be moved as if it is a house item. place it right outside the fire around ( 576, -37, 361 ) /waypoint 576, -37, 361.
The egg will disappear after warming and the quest will auto-complete.
You're well on your way to having your first flying mount! Now it's time to train it. Use the Stormfeather's Pride Griffawn Feather that you received for completing this quest and hail your baby griffawn to begin its training.