Pat steaks dry with paper towels and place on a rimmed baking sheet.
Spray or brush with olive oil and sprinkle with dry rub on both sides. Press the rub down into the steaks. Set aside at room temperature.
Prepare a grill fire to 350° using hickory or pecan for smoke flavor.
Melt butter in a large skillet over medium heat.
Add garlic and mushrooms, cook, stirring often until mushrooms are golden brown.
Stir on fresh thyme, salt and pepper. Keep warm until ready to serve.
Cook steaks over indirect grill fire with the grill closed about 3 minutes. Flip the steaks and continue to cook until desired doneness.
Use a digital thermometer to check the steaks after about 6 minutes. We pulled ours at about 130°.
Remove from grill and rest steaks for 5 minutes.
Top with mushrooms and serve.