Heat grill to medium heat. If possible create an indirect and a direct heat zone. Lightly oil grill grates. Heat 1-2 tbsp oil in large skillet or dutch oven.
Add sliced onions to preheated skillet or dutch oven and slowly cook for 30-40 minutes to caramelize them. Stir occasionally. If the onions are cooking or darkening too fast, move the skillet to a lower heat. The onions should be sweet and have a nice brown color to them. Add thyme to skillet.
If using raw bratwurst, lightly oil the exterior of the meat to prevent sticking to the grill grate or skillet. Cook until firmed up and then move to the hotter side of the grill to brown them up. Do not worry about cooking them thoroughly at this point as they will further cook when braising in the beer.
If using pre-cooked bratwurst, you are just warming them thoroughly. Grill them to get some nice color on them, then add into the skillet with the onions.
Add bratwurst and onions into the same skillet along with beer. Note: Do not poke holes in your bratwurst during the cooking process. Add 1 tbsp of butter to the skillet. Simmer the bratwurst in the skillet until the liquid has reduced approximately 15 minutes. Do not boil.
Lightly butter (optional) surface of rolls and toast on grill surface or on a skillet for approximately 1 minute or until golden brown in color.
Serve bratwurst on a toasted roll with the caramelized onions and other toppings of your choice such as mustard.