In a 12 to 14-inch saucepan over medium heat, heat the olive oil until hot but not smoking. Add the veal pieces and giblets
and cook until evenly browned on all sides, about 10 to 15 minutes. Add the onion, carrot
, celery and parsley and cook until the vegetables begin to soften, about 5 minutes. Season to taste with salt and pepper. Add the tomatoes and the wine and break up the tomatoes with the back of a spoon. Adjust the seasoning. Lower the heat to let the mixture simmer
gently until the wine evaporates, about 10 minutes. In the meantime, roughly chop
the reconstituted mushrooms. Once the ragu has simmered for 10 minutes, add the chopped mushrooms and allow the mixture to continue simmering for another 20 minutes.
Preheat the oven to 400 degrees F.
Slice the cooled polenta 1/2-inch squares. Lightly butter a 9-inch by 9-inch by 3-inch glass or ceramic baking pan. Use 1/3 of the polenta to cover the bottom of the pan with a layer of squares lain side-by-side. Cover with 1/2 of the veal and mushroom ragu
, then top with a layer of 1/4 of the Parmigiano-Reggiano. Begin again with another layer of polenta squares, topped with 1/2 of the chicken liver
mixture, topped with 1/4 of the Parmigiano-Reggiano. Repeat from the first layer of polenta, ending with Parmigiano-Reggiano atop the chicken liver ragu. Grate
some more Parmigiano-Reggiano
over the top, if desired.
Place the prepared casserole
in the oven and bake until the dish is heated through and the Parmigiano on top is brown and bubbly, about 20 minutes. Serve immediately.