Growing up in NY,I ate at alot of pizzerias.That said,only a few handful of places had oil running off the pizza onto the plate,especially when you folded it.I'm talking cheese pizza,not the other toppings.
I wish I knew what cheese they used back then.I have been trying to find the cheese that will give me this as well.
So far,whole milk mozz does it a little bit,but I have to cut it a little thicker than normal, so it melts down white and doesn't destroy itself before the pizza is done.
That said,I had to take the wife and kids to the mall the other day.They wanted pizza for lunch so we ordered 2 large pies from Sbarros there.The cheese only pizza melted and stayed white,did not brown nor burn,and some orange oil kept dripping off the slices when folded.We did not eat all of it...a few hours later in the box,a few slices left over,cheese was still white.Reheated at home,it melted again,more orange oil.
Where I live in my areas KY ,Sbarros is the closest thing to NY style pizza one can get around here.I do not know what cheese they use,I will ask them next time.Yet I have a feeling it may be Grande.I hope they wont play, "Its a secret recipe" ,type of game again.It was pretty good cheese though.