Remove any traces of viscera from the quail cavities. With the tip of a small knife, make a small slit in one thigh of each bird and tuck the end of the other leg into it. Pat the birds dry and set aside.
In a large nonreactive skillet, heat the olive oil over medium flame. Add the onion, chicken livers, bacon, bay leaves, rosemary, and cloves, and sauté about 5 minutes, until the onion is wilted. Push the mixture to the side of the pan farthest from the center of the burner.
Season the quail with salt and pepper, add them to the pan, and brown them on both sides, turning once, about 4 minutes on each side. If necessary, reduce the heat to prevent the onion from burning.
Add the tomato paste, wine, and chicken stock, and bring to a simmer, shaking the skillet and scraping the bottom with a wooden spoon. Cook 5 minutes, turning the quail once. Remove the quail to an ovenproof platter, cover with foil, and keep warm in a low oven. Bring the contents of the skillet to a boil and cook until thick enough to coat a spoon, about 10 or 15 minutes. Pass the sauce through a very fine sieve, pressing down hard on the solids, and pour over the quail. Serve immediately on beds of basic polenta or flanked with lozenges of fried polenta.