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