Combine the rub ingredients, rosemary through the cinnamon, in a small bowl.
Pat dry the steaks and place on a work surface. Sprinkle rub to just cover one side of the steaks, and rub it into the meat. Turn the steaks over and repeat. Leave the steaks out at room temperature for 15 minutes to absorb the rub.
Start the mushroom sauce. Melt 1 tablespoon of the butter in a large skillet on medium heat. Add the minced garlic, sauté until it becomes fragrant, about 1 minute. Stir in the mushrooms, and cook about 5 minutes until the mushrooms begin to sweat.
Pour the red wine into the skillet and stir. Add the thyme, salt and pepper to taste. Cook until the red wine has mostly absorbed into the mushrooms, about 5 minutes. Finish the sauce by adding the reserved tablespoon of butter, stirring the butter to melt in with mushrooms. Keep the mushrooms warm as the steaks grills.
Preheat a grill to medium high as the mushrooms are cooking. When ready, coat the grill with oil spray. Add the ribeye steaks to the grill. Grill covered for 6 minutes, then turn the steaks over and grill covered for another 6 to 7 minutes. 12 minutes total grilling time got our steaks to a good medium rare; depending on your taste and size of your steaks you may want to add a few more minutes grilling time.
When the steaks are done, remove to a platter and let them rest for a few minutes. Then, trim excess fat and slice the steaks crosswise. Plate 3 to 4 slices per person, and top with the mushrooms. Enjoy with a good glass of Merlot