When it comes to expressing the phrase "cooking a storm," there are many alternatives to choose from. One might say "cooking up a horde" to suggest a large quantity of food being prepared, or "cooking with passion" to describe someone putting in a lot of effort and care into their cooking. Another possibility is "cooking a feast," which refers to the idea of a grand meal being cooked for a special occasion or celebration. Other synonyms include "cooking up a frenzy," "cooking like crazy," and "whipping up a storm," each of which has its own unique connotations and nuances. Ultimately, the best synonym will depend on the context in which it is being used and the precise emphasis that one wishes to convey.