How could I resist this challenge!
Ok. So here's how I'd approach this monster. First, you will need something with sufficent surface area to flip this baby. But we'll get to that. Let's first form the patty.
Forget the bread crumbs unless you want a meat loaf or salisbury steak flavor. Do add the egg. It will help reduce shrinkage and keep the burger jucier. Use one large egg per pound of ground beef.
When shaping the patty, to it in the pan you are going to cook it in, or on a plate. Do indent the center as the middle does rise due to contracting protien. You aren't so much worried about the shape as you are making sure the meat is cooked as thoroughly in the center as it is on the rim. Indenting the center will take care of that.
Dont be afraid to season the meat. A light sprinkling of salt on the outside will not dry it out. Over-cooking will dry it out. And as you stated, use a meat thermometer and cook to a minimum temp of 165 degrees F.
The reason you want to make the patty in the pan you will cook it in is that you can then use that pan to flip the burger into a second pan when you need to. I would start the burger on top of the stove, with a lid on it. When the pan is hot, cook for five minutes on one side. While it's cooking, get the second pan hot. Remove the lid from the first pan and carefully flip into the second, lightly oiled pan, taking care not to splash yourself with hot juices. Again cover and cook for five minutes with the lid on. Remove the lid and check the middle temperature with an instant read thermometer. If it reads 160 degrees, your ready for the next step. If you need to cook it longer, do so for another five minutes or so, again covered. Once you bring the meat center up to temperature, place the burger under the broiler for about three minutes to brown. Flip once more into the other pan and broil another three minutes. REmove by flipping the whole burger onto your giant "bun" and top with a buch of tommato, pickles, relish, mustard, onions, whatever you like. Serve open faced on a platter with the top bun sitting beside the burger.
To grill this baby, make the bruger on a plate, again indenting the middle. Fire up the grill with divided banks of charcoal, or only gas burner lit, for the indirect heat method. When the fire is hot, flip the burger onto the grill with the plate, over the coolest part of the grill. Insert a meat thermometer into the burger center, about half-way through and cook as you would a small beef roast, covered of course. Use a flat, metal cooking sheet to flip the burger. Cook until the meat reaches 165 degrees. Remove to a plate and flip onto the bun as previously described.
This burger, cooked by either method should be very juicy, and can very in weight from 1 to 5 pounds. The methods should allow you to make the burger whatever size you want.
The single biggest reason for ruined burgers, is making them the roound shape, IMHO. When the diameter is small compared to the thickness, the outer meat, along with the perimiter becomes dried out by the time the center is thick. For a 4 inch diameter burger, figure a thickness of no more than 1/2 inch. For larger burgers, increase the thickness accordingly. That way, you don't overcook one part before the middle is safely done.
Let us know how you decided to cook your monster burger, and how it turned out. I can't wait to hear.
Seeeeeya; Goodweed of the North