It started with a street punk’s love of nickelodeons and their silent stars, such as Theda Bara and Rudolph Valentino: immigrants, or children of immigrants. Ben “Bugsy” Siegel, whose parents had come to the Lower East Side from Galicia, earned the nickname he hated for the temper that made his face glow and the penchant for violence that all too often made him seem, as one F.B.I. agent later put it, insane “along certain lines.”

As he and his childhood pal Meyer Lansky went from squeezing pushcart peddlers to profiting royally from Prohibition, Siegel often showed a charming side, cutting a swath through speakeasies in dark pin-striped suits, monogrammed shirts, and custom-made alligator shoes. The real surprise, though, was that he wanted to act—and nearly made his dream come true.