Preheat the oven to 400 degrees F. Generously oil a 9-inch pie pan.

Potato Crust: Place 2 firmly packed cups grated raw potatoes in a colander placed over a bowl; toss the potatoes with 1/2 teaspoon salt and set aside for 10 minutes. Squeeze out the excess water. Combine the drained potatoes, 1 large egg, beaten, and 1/4 cup grated onion in a medium bowl. Pat the potato mixture into the oiled pie pan, building up the sides of the crust with lightly floured fingers. Bake for 35 to 40 minutes, until golden brown, brushing the crust with oil after the first 20 minutes to crisp it.

Remove crust from the oven and reduce the temperature to 350 degrees F.

Meanwhile, beat together the eggs, milk, 1/2 teaspoon of the salt, and the pepper in a small bowl; set aside.

Blanch cauliflower. Melt the butter in a large skillet over medium heat. Add the cauliflower, onions, garlic, and 1/4 to 1/2 teaspoon of the remaining salt; cook, stirring frequently, until lightly browned, about 5 minutes. Add the parsley, basil, and thyme; cook, covered, for 10 minutes, stirring occasionally. Remove from the heat.

Layer the baked potato crust with 1/2 of the cheese, then the cauliflower mixture, then the remaining cheese. Pour the milk mixture over the top and lightly dust with paprika. Bake for 35 to 40 minutes, until set. Remove from the oven and serve.