Pre-heat oven to 375 degrees. Brush a pie plate with oil.
Heat oil in small skillet on med-high. Add onion and cook til soft, about 3 minutes. Let cool. In a medium bowl, mix onion and eggs and lightly beat. Whisk in milk, 2 oz. cheese, water, thyme, oregano, salt & pepper and rosemary. Cover bottom of pie plate with broccoli and pour in mix. Sprinkle with 2 oz. of cheese. Bake 50-60 minutes until set. Makes 6 servings.