Preheat oven to 350°F and line a large rimmed baking sheet with foil. Grease 8 cups in a 12-cup muffin tin and set aside. Pour 1 inch of water into a large saucepan and put in a steamer basket. Place broccoli in steamer basket, cover pot, turn heat to high and let cook until broccoli is just tender, 5 to 6 minutes. Let broccoli cool slightly, then chop into small pieces.
In a medium bowl, whisk together milk, cream, eggs and egg yolks. Stir in cheese, salt, pepper and nutmeg. Add chopped broccoli.
Put muffin tin on baking sheet, then ladle egg mixture into prepared muffin cups, filling each cup. Bake until lightly browned and no longer jiggly in center, about 25 minutes. Let cool slightly, then run a knife around each quiche. Put a clean baking sheet on top of muffin pan and invert to unmold quiches. Serve warm or at room temperature.