Preheat oven to 350°F and grease a 9-inch square pan with cooking spray; set aside. Heat olive oil in a large skillet over medium-high heat. Add onion and cook until golden brown, 7 to 8 minutes. Add mushrooms, 1/2 teaspoon salt and 1/4 teaspoon pepper and cook until liquid is absorbed, 10 to 12 minutes; set aside to cool. In a large bowl, whisk together eggs, milk, nutmeg and remaining 1/4 teaspoon salt and 1/4 teaspoon pepper. Add cheese, onion, mushrooms and spinach and mix well. Transfer to prepared pan, spread out evenly and bake until set in the middle and golden brown, about 45 minutes. Let cool 10 or 15 minutes; cut into 24 squares and serve.
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