Use damp kitchen towel to clean mushrooms. Remove stalks from mushrooms. Rub with 1 tablespoon olive oil and place on lined baking sheet with empty sides up.
In frying pan, saute onions in remaining olive oil until soft then add zucchinis, tomatoes and garlic. Add spinach until wilted. Remove from heat and add rosemary, salt, to taste, and pepper, to taste.
Stuff each mushroom with vegetable mixture and sprinkle with cheese shreds. Bake 15-20 minutes. Sprinkle with finely chopped chives.