Drizzle soy sauce and Worcestershire sauce onto the steaks. Sprinkle with steak rub. Rub into the meat on both sides. Let rest at room temperature while you light the egg.
Add lump charcoal to the Big Green Egg, filling to the first line. Tuck a natural charcoal starter into the charcoal and light it. Let it burn for about 10 minutes with the lid open.
In a small bowl, combine the butter, garlic and thyme.
Place the cooking grate into the egg and close the lid. Adjust the temperature to about 550 degrees F. The bottom vent will be wide open and the top vent will be mostly open.
Place the steaks on the grill. Close the lid and cook for 2 minutes.
Burp the egg (open it about one-inch to release some heat). Then, open it all the way. Flip the steaks. Close the lid and cook for 2 more minutes.
Burp the egg. Then, open it all the way. Flip the steaks again. Spoon the butter mixture onto the steaks.
Close the lid. Shut the bottom vent and add the damper top.
For medium-rare steaks, keep the lid closed for 3 minutes. For well-done steaks, leave the lid closed for about 6 minutes. Remove from the egg, and let the meat rest about 5 minutes before slicing.