Cheesecake was a popular Earth dessert made of cream cheese in the form of a cake.
New York cheesecake or Carnegie style cheesecake was one of the many varieties of Earth cheesecakes. Carnegie style was occasionally served aboard Enterprise NX-01 in the early 2150s. (ENT: "Singularity")
On Saturday, August 14, 2152, Chef planned on serving Carnegie-style cheesecake as dessert aboard Enterprise, after a meal of filet mignon, grilled curled onions, and green peas. But when he fell ill, Hoshi Sato took over and decided to cook her family's oden instead. (ENT: "Singularity")
In the late 2250s, cheesecake was one of the many food items vomited out by food synthesizers when Me Hani Ika Hali Ka Po and Sylvia Tilly were in the mess hall aboard the USS Discovery. (ST: "Runaway")
In 2377, when The Doctor temporarily inhabited Seven of Nine's body during an altercation with the Lokirrim, he decided to show Captain Ranek how the replicator worked by replicating a slice New York style cheesecake. Thus, cheesecake became the first thing The Doctor actually experienced "eating," and when Ranek found his reaction (in Seven's body) curious (as he was enjoying himself so much), he asked if he'd eaten it before, and tried a piece himself. (VOY: "Body and Soul")
From the Star Trek Encyclopedia, 4th ed., vol. 2, p. 79, "On very special occasions, the Star Trek: Enterprise art department enjoyed "New York Day", which would be celebrated with food shipped in from Carnegie Deli in the Big Apple, including, of course, New York cheesecake. Yum!"