Preheat oven to 350°F (175°C). Melt butter in a large saucepan over medium-low heat. 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 centre has set.