2) Heat remaining 10ml of oil in the pan and saute the mushrooms until they release all of their water, about six to seven minutes. Remove from heat and cool completely.
3) Spray an oval baking dish with cooking spray. Arrange the bread cubes in the dish. In a large bowl, beat the eggs, egg whites, milk and mustard until incorporated. Add mushrooms, onion-garlic mixture, broccoli, parmesan and mozzarella cheeses, sun-dried tomatoes, thyme, and salt and pepper and stir to incorporate. Pour mixture over bread, making sure liquid saturates bread. Cover with cling film and refrigerate overnight, or at least eight hours.
4) Preheat the oven to 180°C. Remove the cling film from strata and bake for 55 to 60 minutes, or until top forms a light brown crust.