Heat the oil in a skillet set over medium high heat. Add the mushrooms, onion, and garlic, and cook until softened, about 5 minutes. Set aside and let cool slightly.
In a bowl, whisk together the eggs, milk, and cream. Season with salt and pepper. Stir the cooked vegetables and spinach into the egg mixture.
Pour the eggs in to the crust.
Bake for 15 minutes. Then reduce the heat to 350 and bake an additional 30-40 minutes, or until the center of the quiche is set.
If the quiche begins to brown too quickly, cover it with foil.
Let the quiche cool for at least 15 minutes before serving.