In a small bowl mix the rub ingredients together. Massage the rub into both sides of each steak. Let the steaks stand at room temperature for 20 to 30 minutes before grilling.

Meanwhile, prepare the mushrooms. Remove the mushroom stems and discard. Wipe the mushroom caps with a damp paper towel. If using portobello mushrooms, use a teaspoon to scrape out the dark gills.. Cut each mushroom in half, and then cut each half crosswise into 1/2-inch slices. In a 12-inch skillet over medium-high heat, melt 1/4 cup of the butter. Add the mushrooms and garlic, spreading the mushrooms in a single layer. Season with salt and pepper. Cook until the mushrooms are barely tender, 4 to 5 minutes, stirring 2 or 3 times with a spoon. Add the wine and cook until nearly all the wine has evaporated, about 3 minutes, stirring once. Set aside.

With the lid closed, grill the steaks over direct medium-high heat, 450 to 500 degrees F until cooked to desired doneness, 8 to 10 minutes for medium-rare, turning once with tongs or spatula. If flare-up flames occur, move the steaks temporarily over to indirect medium-high heat. Remove steaks from the grill and let rest for 2 to 3 minutes. Meanwhile, reheat the mushrooms over medium heat, adding in the remaining 1/4 cup of butter and heating until the butter has melted. Serve the steaks warm with the mushroom and butter mixture spooned over the top. Add crumbled cheese, if desired.