In a medium size pot, cover the barley with water and bring to a boil with the bay leaf and onion; salt, to taste. Cook until tender, 20-22 minutes, then drain, discarding the bay leaf and onion.
Meanwhile, heat a grill pan, griddle or cast iron skillet over medium-high heat. Dress the beef with the rosemary, garlic, sea salt and pepper. Brush with EVOO and grill for 12 minutes. Let rest for a few minutes, then thinly slice. Toss with the chopped parsley and lemon juice.
In a large skillet, heat 3 tablespoons EVOO, three turns of the pan, over medium-high heat. Add the fresh mushrooms and cook until browned, 10 minutes. Add the celery and shallots and cook, 2-3 minutes. Add the dried mushrooms and deglaze with the Marsala. Add the stock and simmer to soften the dried mushrooms, 8-10 minutes. Add the greens and a grate of nutmeg and cook to wilt. Add the barley and adjust the seasoning, to taste.
Top the warm salad with the sliced steak and garnish with the Pecorino Romano.