Preheat the oven to 350 degrees F.
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.
Pour the sausage mixture into a 9 by 13-inch baking dish, distributing it evenly. Pour the polenta on top, spreading it evenly with a rubber spatula.
Top the polenta with the butter and Parmesan. Bake until golden brown and bubbly, about 30 minutes.
Combine the milk, chicken stock, salt, white pepper, and mace in a large pot over high heat. Bring to a boil, stirring occasionally. Whisk in the polenta. Once the mixture begins to thicken, reduce the heat to medium-low. Cook until the polenta is tender, stirring constantly with a wooden spoon and scraping down the sides of the pot, about 10 minutes. Add the Parmesan and stir to blend. Remove from the heat and stir to cool for 3 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.