It seems there might be a slight misunderstanding here. The term "complimentary cheesecake" does not refer to a specific type of cheesecake. Instead, it could have two different meanings:
Complimentary Cheesecake at a Restaurant: In the context of dining at a restaurant or cafe, "complimentary cheesecake" typically means that the establishment offers a free slice of cheesecake to its customers as a gesture of goodwill or appreciation. It's a way for the restaurant to show their gratitude for your patronage or to celebrate a special occasion.
Complementary Cheesecake Flavors or Pairings: The term "complementary" here refers to flavors or ingredients that go well together. In this sense, a "complementary cheesecake" could mean a cheesecake that is paired with specific toppings, sauces, or accompaniments that enhance its flavor. For example, a classic New York-style cheesecake might be complemented with fresh berries and a raspberry coulis.
If you were referring to a specific type of cheesecake or a particular context, please provide more information, and I'd be happy to assist you further!