Although I've never had a Carl's burger, I can say that simply salting the ground beef doesn't get you far. Of course if you can find particularly high-quality ground beef you won't need to do as much to the patty to make it awesome, (not just talking about fat content, like its a better brand or from a better store than what you've gotten before, maybe even have a butcher's shop grind you up a prime rib steak), you will need much more than salt to get a great burger.
Even if it doesn't make it taste like the Carl's burger, you can make the burger patty better by adding onions sauteed in butter or oil, black pepper, paprika or chili powder (the former for flavour only, the latter for heat), garlic, and if you want it to taste kind of Italian, oregano and basil. All of that together would make a sort of spicy cagun burger.
About the char grilling thing, if you have anywhere outside you can cook, get a little habachi grill. Its all of a few inches high and you can put charcoal briquettes in it and use it like a full sized BBQ.
http://www.drinkstuff.com/products/product.asp?ID=4825
Barring that, get some liquid smoke, it should be in the sauces aisle of most grocery stores. Or a BBQ sauce with smoke flavor added into it. Maybe even throw in a beef bullion cube dissolved in some hot water into the mix. Reduce the salt you add if you do that though, else it'll be way too much.
Last but not least, most mass processed burgers have some sort of binder in it like egg or breadcrumbs, which can effect the taste as well as helping it hold its shape. They aren't all 'evil' substitutions added to rip you off either - I once worked briefly at a place that mass produced burger patties of all qualities and it was all they could do to keep the things together from start to finish. Plain meat just didn't cut it.
Good luck!
She still makes the best sammiches.
