Rinse the barley and add it to a large pot of boiling salted water over high heat. Lower to medium and simmer until tender but chewy, 30 to 35 minutes. Drain.
Take the steak out of the fridge 20 minutes before cooking, pat dry and season with half the salt and pepper.
Heat 1 tsp of the oil in a cast-iron skillet over high heat until very hot. Sear the steak for about 3 minutes per side for medium-rare, 63°C (145°F) in the centre, or 71°C (160°F) for medium.
Rest the steak on a board for 5 minutes, then slice thinly across the grain.
In the same pan over medium-high heat, add the rest of the oil and the mushrooms. Cook without stirring for 2 minutes, then add the garlic, thyme and remaining salt and cook 4 minutes more until browned. Stir in the spinach to wilt.
Build the bowls with barley, mushrooms and spinach and sliced steak, and drizzle with the balsamic.