The Pastrami Dip is a Los Angeles invention. Now, to the average non Angelino, LA is the kind of place you'd expect to invent things like salads and the gourmet barbeque chicken pizza, not something as greasy and messy as this.
That's because there's much more to Los Angeles than Hollywood and other such trendy, 'small salad with dressing on the side' kind of stereotypes. LA is a big city, a working city, an industrial city, a tougher and more hardworking kind of place than tourists tend to see.
There are many places to find a Pastrami Dip in LA and its environs; most independent burger joints and other such places make them. My personal favorite is The Hat, founded in 1952 in Alhambra and with about a dozen restaurants around the city and its environs. 'World-Famous Pastrami' says the sign, and though it's not quite that, it's great food, filling and affordable. Another favorite of many is Johnny's Pastrami, and there are many, many others.
There are, of course, variations, but the classic Pastrami Dip, as served at The Hat, among others, is made thus:
Take a french roll and cut it in half in the standard fashion. Spread yellow mustard generously on the lower half, and place pickle slices on it (about 8 or so). Take the top half, and dip the flat cut side in au jus (beef broth) - just wetting that cut base, not soaking the whole thing. Pile a vast amount of hot pastrami between the two halves. Cut into two halves, and serve.