Gather all ingredients. Preheat the oven to 350 degrees F (175 degrees C).
Melt 2 tablespoons butter in a large saucepan over medium-low heat. Add broccoli, onion, and garlic; cook, stirring occasionally, until vegetables are soft.
Spoon vegetables into pie crust and sprinkle with mozzarella cheese; set quiche on a baking sheet.
Combine eggs and milk together in a bowl; season with salt and pepper.
Stir in remaining 1 tablespoon melted butter; pour egg mixture over vegetables.
Bake in preheated oven until the center of the quiche has set, about 40 to 50 minutes.
Notes
This quiche makes a great vegetarian option for any buffet table.