Remove the steaks from the fridge about 30 minutes to 1 hour before cooking. Place them on a paper towel-lined cutting board and pat them dry with paper towels. Season well on all sides of the steaks with coarse salt and set aside.
In a cast-iron skillet over medium heat, add olive oil and butter, mushrooms, garlic, and salt. Cook for about 3 minutes or until tender. Set aside on a plate.
Increase the heat to high and let it heat up for about 3 minutes. When the pan smokes just a bit, it’s a sign that it’s properly heated. Place the steaks in the hot skillet and cook for about 2 minutes on each side or until the steaks get a nice crust.
Add butter, garlic, and thyme to the skillet. Flip the steaks again and tilt the pan to help the butter spread on the skillet. Using a spoon, pour butter over the steaks. Flip the steaks again and check the internal temperature of the steaks. Medium rare is 135 degrees, medium = 145 degrees, medium well = 150 degrees and well done = 160 degrees. It will depend on how you prefer your steak to be (rare, medium, medium-well, or well done).
When the steaks get to the desired cooking temperature, bring back the mushrooms and serve immediately.