Ellen - I apologize for not getting to this sooner. I have been swamped with my own travels and work. My favorite burger in the Metroplex is not in Dallas, per se. As a matter of fact, it is a bit of a drive from Dallas.
I have recommended this true Roadfood gem to a few people, yet there seem to only be a few on this board who have ever been to this place. My suggestion is to hop in your car and head out to Ponder, Texas - it is about 45 minutes NNW of DFW airport (about 10 miles west of Denton)and hit the Ranchman's Cafe
(aka Ponder Steakhouse). Another compromise that you will need to make is that the burgers are not char-grilled, but fabulous, nonetheless.
Ponder is an historic town - and the steakhouse is located right next to a building that was once a bank robbed by Bonnie and Clyde.
The guy standing up on the left is Dave Ross, the owner. If he is there, and he usually is, he will most likely chat you up - as he seems to know most everyone who comes into the place.
Trust me....you won't be disappointed.
ETA: I have also been to Snuffer's
on Midway and Beltline in Addison and found it to be a pretty good burger, too. I am not sure if they char-grill, either, though.