Preparation

Set the steaks aside to come to room temperature, and pat dry with a paper towel. Season lightly with salt and generously with pepper.

Place a large heavy skillet over medium-high heat, and add 1 tablespoon of the olive oil. When the oil is shimmering, add the onion. Sauté until slightly blackened on the edges and tender-crisp, 1 to 2 minutes. Add the green and red peppers to the pan. Stir the peppers until they are blackened on the edges and tender-crisp, another 1 to 2 minutes.

Add 1 tablespoon of the olive oil to the pan along with the mushrooms, and reduce heat to medium-low. Stir the mushrooms until they are coated with oil and just beginning to soften, about 2 minutes.

Transfer vegetables to a plate and return unwashed skillet to medium-high heat. Add remaining 1 tablespoon olive oil and the steaks, and allow to sear well on the bottom, 1 to 2 minutes. Turn the steaks and sear again for about 2 minutes. Check the steaks with an instant-read thermometer (120 degrees F for rare, 125 for medium-rare, 130 degrees F for medium) or by cutting into them; they should be slightly undercooked. If additional cooking is needed, turn steaks again and cook to taste.

Reduce heat to medium-low, and add the butter. When the butter has melted, add the soy sauce and 1/4 cup water, stirring well and scraping the bottom of the pan.

Return the vegetables to the skillet with the steaks, stirring them to reheat and coat with the sauce. Using tongs or a fork, transfer steaks to a warm serving platter. Spoon the vegetables around and on top of the steaks, and serve.