Preheat the oven to 375°F. Spray a 9 x 13 baking dish with oil.
Place 1 cup of cheese into the baking dish.
Heat the oil in a large nonstick skillet over medium heat; add scallions, mushrooms and red pepper and sauté until vegetables are tender, about 5 to 6 minutes. Add the tomatoes and cook 2 - 3 minutes. Add the ham and broccoli and remove from heat. Spread evenly over the cheese mixture.
In a large bowl combine the eggs, egg whites, milk, salt and pepper and whisk well. Slowly pour over the vegetables in the baking dish and top with remaining cheese.
Bake until a knife inserted near the center comes out clean, 32 to 35 minutes. Let stand 8 to 10 minutes before cutting into 12 pieces.