Season steak with olive oil and salt and pepper on both sides. Place the steak on the grill and cook for about 10 minutes (5 minutes per side) for medium-rare (135°F) doneness. Remove steak from grill and let rest 5 minutes before cutting into it.
While steak is on the grill, heat a sauté pan over medium-high heat.
Add a few tablespoons of olive oil and mushrooms. Sauté mushrooms until they are golden brown, about 5 minutes.
Add red wine, turn heat to high and let the wine reduce in half.
Add thyme and then butter, stirring to incorporate the butter until it has melted.
Season to taste with salt and pepper. Serve the mushrooms over the steak and enjoy.