Ground beef burger patties turn gray not brown
Brown meat tastes good - Anne Burrell


Of course you know this, the browning of the meat is a result of the Maillard Reaction, if you are not getting this result you are probably not cooking at a high enough temperature. 


  Temperatures need to be high to bring about the Maillard reaction, but
  as long as the food is very wet, its temperature won’t climb above the
  boiling point of water. At atmospheric pressure, only high-heat
  cooking techniques can dry out the food enough to raise the
  temperature sufficiently. It’s not the water that stops the reaction,
  but rather the low boiling point...


Too hot, however, and you end up with a patty that is raw in the middle and crusty on the outside. To counter this there are two separate techniques I will use (depending on the weather...) 


In fair weather (using my grill outside) I will heat one side of the grill to "High" and the other side to a medium temperature. First I will 'sear' the burger patty on the High side (both sides of the patty) then move the burger to the medium side, where it can finish more slowly and thoroughly. You can do this in reverse if you like.
In inclement weather (using my oven's broiler) placing the oven rack on the highest setting preheat a cast iron skillet under the broiler for 5 minutes. Place your patties in the skillet and return it to the broiler for 3-5 minutes per side (+/- your patty thickness). Because the broiler is acting on the TOP of the patty rather then the bottom the juices flow away allowing for a quicker maillard reaction. When done set your skillet on the stove top (cool) for a few minutes to let the meat rest and reabsorb some of the juices that should be in the pan at this point. (note: cheese should only be added in the last minute of this technique) 


You can accomplish similar results using a pan on the stove top, but I prefer either of these methods.