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.
Not equivalent as far as being slang is concerned but otherwise, an expression used to positively describe this kind of approach to solve a problem (deal with it bit by bit) is:
- Procéder par étapes
Si l’on veut conserver une expression imagée, je dirais
- Avancer pas à pas
- Avancer (poser) un pied après l’autre
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