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Preheat oven to 350 degrees. In a 9- or 10-inch nonstick heat-proof skillet, heat oil over medium heat. Add mushrooms; saute until browned. Using a slotted spoon, transfer mushrooms to a plate lined with paper toweling. Reserve oil in pan.
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In a medium bowl, whisk the eggs, water and salt.
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Stir in olives, pepperoni, cheese, pepper and cooked mushrooms.
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Reheat skillet over low heat. Pour in egg mixture. Cover and cook until eggs are set around edges, but center is still loose, about 8 minutes. Using a rubber spatula, gently loosen egg mixture from sides of pan.
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Place skillet in preheated oven and bake, uncovered for 12-15 minutes,or until a knife inserted in center comes out clean.
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Transfer frittata to wire rack; let stand 2 minutes. To loosen frittata from pan, slip a rubber spatula between the frittata and skillet. Slide eggs in one piece onto a plate.
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Sprinkle with Parmesan cheese and serve immediately.
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HINT: If skillet has a plastic or wooden handle, wrap it in foil before placing in oven.