Polenta Pie with Sausage: Patissada di Polenta

Name: Polenta Pie with Sausage: Patissada di Polenta
Ingredients: 2 tablespoons, plus 2 tablespoons unsalted butter; 1 onion, finely chopped; 1 carrot, finely chopped; 1 rib celery, finely chopped; Salt and pepper; 1/2 pound pork sausage, ground; 1 pound chicken gizzards, hearts, and cockscombs; 3 ripe tomatoes, seeded and chopped; 1 cup young Parmigiano-Reggiano, grated; 2 ounces dried mushrooms, soaked to rehydrate, squeezed dry, and chopped; Soft polenta, recipe follows; 4 cups water; 2 tablespoons salt, or to taste; 1 cup polenta or cornmeal; 1/2 cup stracchino, cut into cubes