Bring a large pot of salted water to a boil. Add potatoes and cook until tender but still firm, about 15 minutes; drain. Meanwhile, place broccoli in a steamer over a couple of cms of boiling water, and cover. Cook until tender but still firm, about 2 to 6 minutes. Drain and set aside.
Mash the potatoes with milk and salt. Brush a deep 23cm pie dish with olive oil and press the potatoes in. Brush with remaining olive oil. Bake in preheated oven for 30 minutes or until lightly browned.
Arrange onions, broccoli and cheese in the potato base. Whisk together the eggs, milk, salt, pepper and nutmeg. Pour over broccoli and cheese.
Bake in preheated oven for 30 to 40 minutes, until slightly puffed and cooked throughout. Allow to cool for 10 minutes before serving.