A galley structure for an aircraft cabin includes double-depth cart bays capable of stowing an outer full-size cart in front of an inner fell-size cart. An extraction and retention (E&R) system is mounted to a sidewall of the double-depth cart bay and includes a stowable retainer arm and fixed extractor arm coupled to and articulable via an extraction handle that may be pulled or pushed out of or toward the cart bay. When the outer cart is removed, the inner cart can be brought forward for extraction via the extractor arm (the inner cart extractable once the retainer arm is stowed) and returned to its inner stowed position via the retainer arm (in both cases, by pulling or pushing the extraction handle). The extraction handle includes a retainer actuator for stowing or deploying the retainer arm as needed.