Two New York pizzerias, both alike in dignity, prospered in the Big Apple as coal-fired descendants of the same famed Italian ancestor: Pasquale “Patsy” Lancieri, the inventor of by-the-slice pizza.

Mention the name Patsy’s to almost anyone who appreciates Italian food, music and New York history, and the conversation is almost certain to turn to Francis Albert Sinatra, the Chairman of the Board, ...