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Douglas Harper's Etymology Dictionary
sous chef

early 19c., from French sous, from Old French soz (10c.), from Latin subtus "under, below" (see sub-) + chef.

Wikipedia
Sous chef

A sous-chef de cuisine ( French for "under-chef of the kitchen") is a chef who is "the second in command in a kitchen; the person ranking next after the head chef." Consequently, the sous-chef holds a lot of responsibility in the kitchen, which can eventually lead to promotion to becoming the executive chef. A sous-chef is employed by an institution that uses a commercial-grade kitchen such as a restaurant, hotel, or cruise ship.

The sous-chef has many responsibilities because the executive chef has a more overarching role. Sous-chefs must plan and direct how the food is presented on the plate, keep their kitchen staff in order, train new chefs, create the work schedule, and make sure all the food that goes to customers is of the best quality to make customers happy.

Sous-chefs are in charge of making sure all kitchen equipment is in working order. They must thoroughly understand how to use and troubleshoot all appliances and cooking instruments in the event of a malfunctioning cooking device. Sous-chefs are in charge of disciplining any kitchen staff who may have acted against restaurant policy. Incentive programs are commonly used among sous-chefs to encourage their staff to abide by rules and regulations, and motivate them to work efficiently at all times. Under the oversight of the sous-chef, downtime should be used for prepping, cleaning and other kitchen duties. They are responsible for inventory, product and supply rotation, and menu tasting. Sous-chefs need to be responsive and have the ability to improvise when a problem arises while the restaurant is busy. They must also ensure safety precautions and sanitary provisions are taken to ensure a safe and clean working environment.