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Preheat oven to 375 degrees F.
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In large sauté pan over medium heat, add butter and 1 tablespoon olive oil.
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Place mushrooms in single layer and stir occasionally until mushrooms are evenly browned. Transfer browned mushrooms to bowl.
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In same sauté pan, drizzle remaining olive oil. Add sliced shallots and stir frequently for one minute. Return mushrooms to pan.
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Add garlic and chives and cook one minute. Remove from heat and add salt and pepper to taste.
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In 9-inch glass pie dish, roll out room temperature pie dough and press firmly. Trim excess dough and crimp edges, if desired.
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Layer mushrooms into pie crust. Crumble 2 ounces goat cheese over mushrooms. Top with ¼ cup parmesan.
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In large bowl, vigorously whisk eggs, heavy cream, milk, nutmeg, salt and pepper. Gently fold in the remaining goat cheese and parmesan.
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Pour egg mixture into pie pan.
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Bake 35 to 40 minutes or until egg is just set.
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Let quiche rest for at least one hour before serving. Serve warm or at room temperature.