TV show; The Making of the Mob

I saw this show listed so, being an affectionado of old gangster lore I flipped over to it and watched it muted to see if I would recognize the event depicted. The first scene I saw was of a balding guy with a goatee getting a shave. I thought, if that’s supposed to be Albert Anastasia they didn’t try very hard. Sure enough, the barber excuses himself, and two guys come in and blast away. In this retelling, Albert pulls a gun and returns fire. Funny enough, the old gangbuster Rudy G was one of the talking head commenters.