Preheat the oven to 375 degrees F (190 degrees C). Place the onion and olive oil into a 9 inch deep-dish pie plate. Bake for about 15 minutes, or until onion is tender.
Place the lentils and water into a saucepan, and bring to a boil. Cook for about 20 minutes, or until lentils are tender. Drain most of the water off, then place the broccoli florets on top of the lentils. Cover and cook for about 5 minutes. This will dry the lentils, and cook the broccoli.
Transfer the lentils, broccoli and tomatoes to the pie plate with the onions, and stir to evenly distribute each item. Stir in cheese at this time if using. In a medium bowl, whisk together the eggs, milk, salt, pepper, and Italian seasoning. Pour over the ingredients in the pie plate.
Bake for 45 minutes in the preheated oven, or until the center is firm when the quiche is jiggled. Cool for a few minutes before slicing and serving.
