RE: Eggs
It's one egg and it's a bonding agent. It doesn't turn your burger into meatloaf... All it is doing is holding all of the ingredients together. Try it before ya knock it, gents (though you probably already have if you've ever ordered a burger at a restaurant). You won't even know it was ever there when they come off the grill, aside from your burger not falling to shambles. "Restaurant quality" burger recipes were requested, and you'll find many restaurant quality burger recipes to have egg in them.
I get it, and I'm sure you make a nice burger. Maybe my comment, which I made in jest, was a bit off putting... I apologize if I offended anyone.
For me, I dont want all the ingredients in my burger, so I don't need a bonding agent. A good burger can stand alone for the most part and whenever I want cheese, or peppers, mushrooms, onions, etc; I'll put them on top the burger as part of the sandwich, rather than part of the patty.
I prefer to form the patties by handling them as little as I can. I salt them and let them rest for as long as possible - exactly the same as I treat my steaks. If there's any salt left when I'm ready to cook, i'll brush it off. At that point, I grind up some black pepper and dust each side giving a little pat to press it in. An aside - if you have a mortar and pestle and you like pepper, get yourself some nice peppercorns to grind up. Trust me.
I place the hardwood charcoal off to one side, enough that I have a place to pull the burgers out of the direct heat. When the coals are ready and the fire is nice and hot, the patties go on to get seared. When the first side is seared, flip and repeat. Watch the time though because it'll happen quicker on the side two. Once side 2 is seared appropriately, off the heat to the side. I Use a quick read thermometer to get get the burgers where I want them to be. Once they're done, pull em off and let them rest.
While the burgers are off the heat, sometimes I like to grill up some chilis to put on top with a blanket of good cheddar.
A super easy side coudl be achieved by tossing some fresh asparagus with evoo, salt and pepper and roll them onto the heat for a couple minutes. I assume you've already got some diced potatoes roasting in the oven with your preferred seasoning - I like reds with rosemary and garlic. Or sweet potato with jerk seasoning.
Don't underestimate the importance of good bread. I like to toast the buns on the grill so they can hold up a little better to the juicy burgers.
Now you've got a pretty fail safe meal and it's super easy.
Really, I use this same method for steaks as well and it never disappoints