Preheat oven to 375°.
In a medium bowl, combine potaoes, 1 T. olive oil, 1/2 teaspoon salt and 1/2 teaspoon pepper. Press potatoes into the bottom and sides of a 10 inch deep dish pie pan coated with cooking spray. Bake for 10 minutes.
In a large skillet, heat remaining 1 T. olive oil over medium heat. Add mushrooms and onions and cook for about 6 minutes or until tender.
Add the remaining salt and pepper, spinach, thyme and garlic. Cook for a few more minutes until spinach wilts. Cool slightly then stir in eggs and goat cheese.
Pour mushroom mixture over potatoes. Bake for 30 minutes or until eggs are set.
Cool for 5 minutes before serving.