Combine the garlic, rosemary, salt and pepper and enough olive oil to make a somewhat dry paste. Divide the paste evenly among the 8 pieces and let sit, covered and refrigerated, for 2 hours.
In a Dutch oven, heat 3 tablespoons olive oil over high heat until smoking. Brush the excess rub from the bird and sear each piece of meat on all sides in the hot oil. Remove seared meat to a plate lined with paper towels. Add the onions, the mushrooms and the pancetta and cook over high heat until onions are golden brown and fat has been rendered from pancetta. Drain the excess oil, then add the wine and stir the bottom of the pan with a wooden spoon to dislodge the browned bits. Add the tomato puree, chicken stock, sugar and chili flakes and bring to a boil. Return the chicken to the pan. Cook for 20 minutes, covered, then 15 to 20 minutes more, uncovered. Remove from heat, cut each quarter in half, and divide meat evenly among 4 warmed dinner plates, giving each plate 1 section of breast and 1 section of leg. Top with the sauce and serve immediately.