There are a few basic items on which research at PFI is never closed.  New recipes for hamburgers are always popping up, and here is one from a Greek family who have run hamburger joints since the late twenties.  The ingredients are pictured above, and no, the beef broth is not a mistake. 

First, we'll prepare the accessory items.  Chop up an onion, and if you don't know how to do so quickly and without tears, watch closely!  Peel and halve the onion; slice each halve into strips almost but not quite from one end to the other...

turn and slice through the layers perpendicular to the strips and the onion will fall naturally into chopped bits

Slice up the buns and fry them in a little olive oil in the same pan used to cook the onions.

Fry the buns till golden brown and studded with onion bits, and set aside.

Now mix up 90/10 (80/20 also works) fresh hamburger meat with a raw egg, salt and pepper.  Although not strictly necessary, smart money uses fresh ground pepper, a little soy sauce instead of salt, a liberal sprinkling of garlic powder, and possibly a slug of Trappey's "Red Devil" cayenne pepper sauce.

Now, pay close attention!  Mix ketchup with as much beef broth as possible without losing the colloidal consistency of the sauce.  The beef broth fortifies the beefy taste.

Keep it ketchup-like or it will just make the hamburgers wet and soggy.  While the meat cooks, the external coating of ketchup will carmelize, which it won't do if there's too much broth in the sauce.

Give each ball or patty a complete bath in the sauce, and bring out to the grill because you are going to baste the cookies hamburgers with it.

Preheat the grill then turn down to low to cook, turning once and basting.

Fully assembled with fried onions, freshly made French fries, and ready to eat.