Pat your steaks dry and let them sit at room temperature for 20 minutes or so as you slice the mushrooms and heat the pan. Shower them with salt and pepper.
Set a large, heavy skillet over medium-high heat (cast iron is ideal), and add a generous chunk of butter—a couple tablespoons, at least. Cook the mushrooms, sprinkling them with salt, until they soften and start to brown. Transfer them to a bowl.
Add another chunk of butter to the pan, and when it melts and foams, add the steak(s). (If you cook more than one steak at a time, make sure the pan isn’t too crowded, so that they are able to brown properly.)
Add the thyme leaves or whole sprigs of rosemary to the pan and cook for about 4 minutes per side for medium-rare, flipping and basting with butter (tip the pan occasionally to help it pool) until cooked to your liking.
Return the mushrooms to the pan for a minute to warm them through, pouring any juices that have collected in the bottom of the bowl over the steak.
Serve topped with the mushrooms, along with any juices that have accumulated in the bottom of the pan.
If there are plenty of browned bits, add a small splash of water, beer, wine or even cream to help loosen them, and pour the sauce over the steaks as well.