There are in fact at least 2 traditional NY white pies that have been around for decades. They come from Lombardi's and Totonno's. The Lombardi version has become the basis for what most New Yorkers consider as white pie because it is ricotta based, Totonno's is more personalized because Jerry Pero made his white pie strictly with hand-made fresh mozzarella. It was not on his menu and he only made for special people--like me
The Lombardi version:
build a pizza in the following order:
chopped fresh garlic
fresh mozzarella, sliced
ricotta impastata* in dollops
Parmesan, grated (optional)
olive oil drizzled over all before baking
* Ricotta impastata is key to authentic NY White pie as it is cream based instead of milk based and it is smooth, thick and very creamy. It has a much lower moisture content than regular ricotta and an incredibly rich flavor that is hard to beat. Admittedly, it is very difficult to get outside of NYC--even on a commercial basis. It is not sold retail. Commercial varieties are Pollyo's TLC and Grande's Il Pastaio. You can substitute regular whole milk ricotta that has been squeezed through some cheese cloth and allowed to drip off the excess moisture with excellent results.
Jerry Pero used to make this for me at Totonno's, they still make this pie by request, but it is not as heavenly as when Jerry used to make it for me, nonetheless, it is still a masterpiece.
For the pizza:
Lots of sliced fresh mozzarella
fresh garlic--sliced paper thin (Jerry insisted the garlic be sliced with this tiny paring knife just prior to preparing the pizza. The exact thickness of the garlic was always a point of contention between Jerry and Cookie (his niece and current owner of Totonno's) and they would fight like cats and dogs over it. It was like a comedy routine out of SNL.
plenty of olive oil drizzled on top. Jerry used a gallon container of Berio olive oil which he generously waved over the pizza.
The result was a sea of molten cheese flavored to perfection, paired with his ethereal crust, it was almost a religious experience... The version they produce at the pizzeria today is damned good, but lacks the masters touch. I have this pizza on my menu as an homage to Jerry. My guys do a great job with too, however when I want that pie, I make it myself and handle the dough in the same way I learned from Jerry. I also bulid the pie and bake it exactly as he taught me and the results are very nearly as sublime as his. I always think of him whenever I make it.
So much of what the old timers were about goes well beyond the mere recipe, their touch and sense of timing and baking is hard to teach someone else.