Preheat oven to 375°.
Combine potatoes, 2 teaspoons olive oil, 1/2 teaspoon freshly ground black pepper, and 1/4 teaspoon salt in a medium bowl. Press potatoes into the bottom and up sides of a 10-inch deep-dish pie plate coated with cooking spray. Bake at 375° for 10 minutes.
Heat remaining 1 teaspoon oil in a large nonstick skillet coated with cooking spray over medium-high heat. Add mushrooms and onion to pan; sauté for 6 minutes or until tender. Add the remaining 1/2 teaspoon pepper, remaining 1/4 teaspoon salt, spinach, thyme, and garlic; cook 3 minutes or until spinach wilts. Cool slightly; stir in egg substitute and cheese.
Pour mushroom mixture over potato mixture. Bake at 375° for 30 minutes or until set. Cool 5 minutes; cut into 6 wedges.