Heat oil in 12-inch nonstick skillet over medium-high heat. Cook onion and mushrooms in oil, stirring frequently, until tender.
Stir in tomatoes, barley and thyme; reduce heat to low. Cover and simmer 12 to 15 minutes, stirring occasionally, until barley is tender.
Stir in beans, spinach and 1/2 cup of the cheese; cook until hot. Sprinkle with remaining 1/4 cup cheese.