The night before: Heat a small amount of olive oil in a medium skillet and sauté the onions over medium-low heat until golden brown, about 10 minutes.

While the onions are cooking, steam the potatoes in a small amount of water in a covered pot until they are tender.

Add the steamed potatoes to the onions, season with salt and pepper, and cook the potato/onion mixture until the potatoes are browned.

Set aside in a covered bowl.

Cook the sausage, breaking it up as it cooks, until it is no longer pink. Drain and cool.

Refrigerate the onion-potato mixture and the sausage separately overnight.

The next morning: Preheat the oven to 350°F.

To prepare the polenta, bring 3 cups of water to a boil.

Whisk in the cornmeal and cook the mixture over low heat, stirring occasionally, until thick and smooth (approximately 7 minutes).

Pour the polenta into an ungreased 9x13-inch baking dish. It will begin to get firm as you scramble the eggs.

Beat the eggs in a small bowl and season with salt and pepper.

Heat butter or oil in a skillet over medium heat.

Pour in the eggs and scramble them until slightly firm but still wet.

Remove from the heat. (The eggs will finish cooking in the oven.)

Spread the potato mixture, sausage, parmesan and Cheddar over the polenta.

Pour the eggs on top of the entire dish.

Bake until heated through and the cheese is melted and bubbly, about 15 to 20 minutes. Cool slightly, then cut and serve.