Divide and conquer: Boil the barley separately while you move forward with the soup to get it all done in just under 30 minutes. Bring a medium saucepan of water to a boil, add the barley and boil until just tender, 20 to 22 minutes. Drain and reserve.
Meanwhile, in a soup pot, heat the EVOO, 4 turns of the pan, over medium-high heat. Add the fresh mushrooms and cook until browned, then add the onion and garlic and cook until soft, 12 to 15 minutes total. Add the kale and cook to wilt; season with salt, pepper and the nutmeg. Stir in the stock, a couple of cups water and the dried mushrooms; bring to a boil. Lower the heat to simmer and cook until the dried mushrooms are tender, 7 to 8 minutes. Stir in the reserved barley. Serve the soup in shallow bowls and top with the pecorino-romano.