In a medium pot, cover the barley with water and bring to a boil with the bay leaf and onion; salt to taste. Cook until tender, 20 to 22 minutes, then drain, discarding the bay leaf and onion.
Meanwhile, heat a grill pan, griddle or cast-iron skillet over medium-high. 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 tbsp. EVOO, 3 turns of the pan, over medium-high. Add the fresh mushrooms and cook until browned, 10 minutes. Add the celery and shallots and cook, 2 to 3 minutes. Add the dried mushrooms and deglaze with the marsala. Add the stock and simmer to soften the dried mushrooms, 8 to 10 minutes. Add the greens and a grate of nutmeg and cook to wilt. Add the barley and adjust the seasoning. Top the warm salad with the sliced steak and garnish with the pecorino-romano.