Please, help me to find an appropriate equivalent!
Edit: To "knife and fork" a problem, in the English language, means to "give it a try," perhaps without expecting good results, or with low expectations. Source: The Guardian
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If you want to keep a food-related word, the verb saucissonner may be adequate. Literally, it means "to divide in slices, like a sausage", but is frequently used in French office slang.
It sometimes has a negative connotation, as it can imply that the "slicing" was done for questionable reasons, or with no transparency, or just for the sake of splitting responsibilities, etc.
Le management a décidé de saucissonner le projet, et il y a maintenant 5 chefs de projet et 5 équipes qui travaillent dessus.