The Cook Book has gone through many changes in it's history as a magic item but the current iteration simply fills the player's hunger bar to full while held.
The Aura: Fullness and Cost Reduction X don't have any apparent effect, however the Cook Book's singular effect is to fill the players hunger when held in either the main hand or off hand. This effect does not extend into saturation.
How to Get it
This magical book can only be attained through magic chests!