Make the risotto: In a 10 to 12-inch saucepan, melt 3 tablespoons of the butter. Add the onion and sweat until soft and translucent, about 5 minutes. Stir in the rice and cook over medium-high heat. Using a wooden spoon, stir continuously until the rice is coated in the butter and begins to turn translucent, about 2 minutes. Be careful not to let the rice burn. Keeping the heat at medium-high, begin ladling the hot broth into the rice, about 2 ladlefuls at a time. Constantly stir with the wooden spoon until the rice has almost absorbed all of the broth. Continue adding the broth bit by bit until the rice is al dente or tender, about 20 minutes. Once the rice is cooked, season with salt and pepper. Remove from the heat and immediately add the remaining tablespoon butter and 3/4 cup Parmigiano. Stir to thoroughly combine and keep warm until ready to serve.
Dredge the chicken liver pieces through the flour until well coated. Shake to remove any excess flour and set aside.
In a 12-inch saucepan, heat the olive oil over a medium-hot flame. Add the chicken livers and cook until golden brown on all sides, about 5 minutes. Pour the wine over the chicken livers and let cook until the wine evaporates, about another 4 to 5 minutes. Season, to taste, with salt and pepper. Add the chicken stock. Keep cooking over a medium flame until the chicken livers are completely cooked, about 3 minutes more. Let the broth bubble so that the sauce thickens; there should almost be no sauce in the pan, just a few droplets to keep the livers moist.
Serve the chicken livers immediately, in the center of a serving platter, accompanied by the hot risotto. Garnish with parsley.