Preheat the oven to 350F. Place the oil in a large, heavy skillet over medium-high heat. Brown the rabbit pieces in batches until golden, about 5 to 7 minutes per side, sprinkling with salt & pepper. Place the browned rabbit into a shallow baking pan. Add the onion to the skillet and cool over low heat for 7 to 10 minutes to soften. Add the garlic and cook 2 minutes more, stirring. Add broth and raise the heat; bring to a boil, scraping up the browned bits on the bottom of the skillet. Reduce the heat; add the rosemary and cook sauce for 2 minutes longer. Pour the sauce over the rabbit and bake for 45 minutes. To serve, place rabbit pieces on a serving platter and pour all remaining pan juices over top. Sprinkle with chopped parsley and serve immediately. Serves 4.