Preheat the oven to 450 degrees F. Bring the chicken stock up to a boil. Stir in the cornmeal and cook the polenta for about 20 to 25 minutes over low heat stirring often. Spread the polenta out onto a parchment lined 1/2 sheet pan. Let the polenta cool completely. Soak the mushrooms in 4 cups warm water for about 30 minutes. Drain the mushrooms and reserve the liquid. Squeeze the mushrooms dry and chop. Set the mushrooms aside. In a large saute pan, heat 3 tablespoons olive oil, butter and ham fat. When the oil is hot, add the vegetables and saute for 2 minutes or until wilted. Season with salt and pepper. Add the ground sausage and continue to cook for about 4 to 6 minutes or until browned, stirring constantly. Reduce the heat to low and stir in the tomatoes and continue to cook for 15 minutes. Add the mushrooms and reserved mushroom liquid. Season with salt and pepper. Continue to cook for 15 minutes. Remove from the heat. Cut the polenta into 3-inch rounds. Butter a 8 by 8 by 2-inch baking dish. Line the bottom of the dish with the polenta rounds. Spread a thin layer of the meat sauce over the polenta. Dot the sauce with a couple of tablespoons of butter. Sprinkle some of the cheese over the top. Repeat the process until all the ingredients are used. Place the pan in the oven and bake for about 6 to 8 minutes or until the top is golden and heated through.