Bring a large pot of water to a boil, salt generously and add the greens. Cook for 1 to 4 minutes until just tender. Place in a bowl of ice water then drain, squeeze out water and chop.
Heat the olive oil in a large nonstick skillet over medium heat and add the shallot. Cook, stirring, until tender, about 3 minutes. Add the mushrooms and cook, stirring often until tender. Salt and pepper to taste. Add the garlic and rosemary and cook for one additional minute. Add the greens and cook for one final minute.
Whisk together eggs and milk. Add 1/2 tsp. salt and fold in cheeses and mushroom mixture. Scrape into the pastry shell and bake for 35 minutes or until browned and sizzling. Serve warm or at room temperature.