Remove the steaks from the refrigerator, then sprinkle on both sides generously with salt and place on a wire rack over a sheet pan. Allow to come up to room temperature, about 2 hours.
Preheat a grill for two-zone cooking with high heat on one side and no heat on the other side. (The overall grill temperature should be 325 degrees F on the grill grates.)
Using a paper towel, wipe off any excess moisture and salt from the steaks.
Start the steaks on the indirect heat side of the grill. (The target grill temperature should be around 250 degrees F.) Cover and grill the steaks, flipping once, until the internal temperature reads 125 degrees F (10 degrees away from finished target temp), about 45 minutes to an hour.
Meanwhile, combine the butter, thyme, Worcestershire, a pinch of salt and some pepper in a small bowl. Spread one spoonful of the butter directly on your serving board underneath where each steak will be placed. Do this before you get your steaks on the grill so that when they come off, you can set each steak on a spoonful of the butter. Set aside the remaining butter for the top of the grilled steaks.
Move the steaks to the direct-heat side of the grill and sear until the internal temperature reads 135 degrees F, 2 to 3 minutes per side. Place the steaks on the resting butter and use a fork to spread the remaining butter over the steaks. Let the steaks rest for 10 minutes before slicing.