In a large nonstick frying pan, heat 1 tablespoon of the oil over moderately high heat. Add the fennel, 1 teaspoon of the rosemary, and 1/4 teaspoon of the salt. Cook, stirring frequently, until the fennel is golden brown and almost done, about 12 minutes. Add the broth and bring to a boil. Cover, reduce the heat and simmer until the fennel is tender, about 3 minutes. Remove the fennel and the cooking liquid from the pan.
Wipe out the pan and heat the remaining 1 tablespoon oil over moderate heat. Season the chicken with the remaining 1/4 teaspoon salt and 1/8 teaspoon of the pepper. Add the chicken to the pan with the remaining 1 teaspoon of rosemary and cook until brown, about 5 minutes. Turn and cook until almost done, about 3 minutes longer. Add the garlic; cook, stirring, for 30 seconds. Add the fennel and its cooking liquid and the remaining 1/8 teaspoon pepper. Bring to a simmer. Cover the pan and remove from the heat. Let steam 5 minutes. Stir in the parsley.
Menu Suggestions: Soft polenta is an appropriate accompaniment to this Italian-style dish. Mashed potatoes are another good match.
Wine Recommendation: The fennel and the rosemary will pair especially nicely with a full-bodied red wine that has a hint of sweetness, such as a Rioja from Spain.