Remove the steak from the refrigerator well in advance so it comes to room temperature and cooks evenly. Brush the mushrooms clean and slice them; trim the woody ends from the asparagus.
Heat half the olive oil in a skillet over high heat and brown the mushrooms with the minced garlic. Add the asparagus and sauté for a few minutes until just tender; season with salt, pepper and some thyme.
Pat the steak dry, season with salt and pepper and fry it in the remaining oil for approximately two to three minutes per side for a medium-rare result. Let the meat rest for a few minutes under foil, slice it diagonally and serve with the vegetables.