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Heat the olive oil in a large skillet over high heat. Add the sausage and cook until browned, breaking up clumps with a wooden spoon, about 5 minutes.
Transfer the sausage to a paper towel-lined plate.
Add the onions and bell peppers to the pan and cook until they begin to soften, about 2 minutes. Add the garlic and Italian Essence and cook for another 2 minutes.
Return the sausage to the pan, stir to mix, and cook for another minute. Add the tomatoes and stir to mix. Cook until most of liquid has evaporated, about 7 minutes. Season with the black pepper and salt.
Top the polenta with the butter and Parmesan. Bake until golden brown and bubbly, about 30 minutes.
Meanwhile, combine the eggs and egg yolks in a medium bowl and whisk until frothy.
Add 1/2 cup of the polenta to the eggs (to temper) and whisk to blend. Gradually add the egg mixture to the rest of the polenta (in about 3 additions), stirring constantly. Continue to stir vigorously for another 2 minutes. Reserve for the casserole.