Cook the green beans in lightly salted water for five to six minutes until tender-crisp, then drain them. Remove the steak from the refrigerator well in advance so it reaches room temperature.
Heat the olive oil in a frying pan until it is very hot and cook the steak for about two minutes per side for a medium-rare result. Season with salt and pepper, loosely wrap it in foil and let it rest.
In the same pan, fry the mushrooms with the pressed garlic and thyme in the butter until golden brown. Stir in the green beans to warm them through. Slice the steak and serve with the mushrooms and beans.