Preheat oven to 350°F (180°C). Place pie shell on parchment-paper-lined baking sheet. Arrange half of the broccoli, ham and cheese in the bottom of pie shell. Whisk together eggs, milk, nutmeg, salt and pepper; pour into pie shell. Top with remaining broccoli, ham and cheese. Bake until eggs are set, 45 to 50 min. Let stand 10 min. before cutting.
To blanch broccoli, plunge into boiling water for 2 min. Cool in cold water; drain well and pat dry.