You can buy the Apparatus to instantly complete whatever tasks the workers are currently doing. The Apparatus uses Z stars that are found on Star Island, given as quest rewards, and various other places throughout the game. Make sure no other workers are doing anything except the cooks (or whatever you're trying to speed up at that time) because it will speed up ALL workers at once and cost you 1 star per task. For example, if you had a set of cooks working on their 3 recipes, that would cost you 3 stars. But if you used it while a woodcutter and stoneminer were also working, that would cost you 9 stars. Imo, the stars should be saved as much as possible so as not to waste them.