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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.
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.