Over medium-low heat melt butter in a large saucepan. Add onions, garlic and broccoli. Cook slowly, stirring occasionally until the vegetables are soft. Spoon vegetables into crust and sprinkle with cheese.
Combine eggs and milk. Season with salt and pepper. Stir in melted butter. Pour egg mixture over vegetables and cheese.
Bake in preheated oven for 30 to 50 minutes, or until center has set.
