Drain the potatoes and squeeze dry. Add about 1/2 t salt, 1 egg and about 1/4 cup (or more to taste) grated onion. Pat potato mixture into well-oiled 10-inch pie pan and bake at 400 degrees F. for 30 minutes. Brush potato crust with oil, reduce oven temperature to 375 degrees F. and bake for another 5-10 minutes, until crust is brown.
While crust is baking, saute about 1 cup chopped onion and garlic in butter. If you like a lot of onion and garlic, use more. Add broccoli, about 1/2 t salt, basil, a dash of thyme, and cook covered, stirring occasionally, for a few minutes.
Spread half of cheese over baked crust. Top with sauteed vegetables and remaining cheese.
Beat together remaining 3 eggs and milk, and pour over vegetable/cheese mixture. Sprinkle paprika on top. Bake at 375 degrees F. for 35 to 40 minutes until custard is set.
NOTES: A wonderful vegetable pie -- This recipe is originally from the _Los Angeles Times_. It takes a lot of time to make, but it's quite good. Yield: serves 3-4.
This recipe can be made in two stage advance and then can make the vegetables: you can make the crust in topping and bake it later.
An electric grater is a real time-saver for the crust ingredients.