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Preheat oven to 180°C (350°F).
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Arrange half of the broccoli, ham, and cheese in the bottom of pie shell.
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Whisk together eggs, milk, nutmeg, salt, and pepper; pour into pie shell.
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Top with remaining broccoli, ham and cheese. Bake quiche until eggs are set, 40 to 45 minutes. Let stand for 10 minutes before cutting.
Chef’s secret:
To blanch broccoli florets, plunge into boiling water for 2 minutes. Cool in cold running water; drain well and blot dry with paper towels.