Rinse the steak, pat dry, and season with salt and pepper.
Heat the cast iron skillet until hot, then add one tablespoon of oil. Add the steak and cook for two to three minutes, depending on thickness. Flip and cook for another two minutes. Use the meat thermometer to determine the desired doneness and remove to a plate and cover with foil. Note: below is the temperature chart for doneness.
Add the remaining tablespoon of oil and add the green beans and mushrooms. Cook until the mushrooms start to brown. Remove and plate with the steak. Remove the pan from the heat and let the pan cool slightly.
Add the lime juice, brown sugar, fish sauce, and butter. Stir until the butter melts and the brown sugar has dissolved.
Pour sauce over the steak and beans and serve.