Combine the beer, sauerkraut with any juice from the package, and mustard in a lasagna-size disposable aluminum pan. Stir until the ingredients are well combined. Add the thyme sprigs and bay leaves (if using) and nestle the sausages into the sauerkraut and beer.
Place the tray on the hot side of the grill and cook until the beer comes to a low simmer (a few bubbles), about 4 minutes. Slide the pan to the cooler side of the grill. Cover the grill with the vents over the bratwurst. Cook with open vents for 18 to 20 minutes, turning once after the first 10 minutes. Using an instant read meat thermometer, check the internal temperature of the bratwurst after 18 minutes of total cooking time and remove from the heat once they register 140 to 145 degrees F.
Open or remove the lid from the grill and using tongs, lift the bratwurst from the sauerkraut and place them directly on the oiled cooking grate over the hot side of the grill. If using a gas grill, reduce heat a little, if needed, to avoid burning. If there is not enough space, just pull the pan off the grill, set it aside, and cover it loosely with a sheet of aluminum foil to keep the sauerkraut warm. Cook the brats, turning occasionally, until well browned, crisp, and they reach an internal temperature of 160 degrees F, about 3 to 5 minutes total. Return the bratwurst to the pan with the sauerkraut for serving.
Toast the buns over the hot side of the grill or your oven’s broiler.
Serve the bratwurst on toasted buns with the sauerkraut from the pan and optional toppings.