Preparation Melt 3 tablespoons butter in large nonstick skillet over medium-high heat. Add onions and 3 tablespoons sugar. Cook until onions are golden, stirring often, about 15 minutes. Reduce heat to medium-low. Add wine and cook until onions are very tender and mixture is reduced to thick jamlike consistency, stirring frequently, about 40 minutes. Set compote aside. Preheat oven to 450°F. Melt 2 tablespoons butter in heavy large skillet over medium-high heat. Add hen quarters and brown well on all sides, about 8 minutes. Place hen quarters on rimmed baking sheet (do not clean skillet). Sprinkle hens with salt and pepper. Bake hen quarters until cooked through, about 20 minutes. Transfer hen quarters to bowl; cover to keep warm. Add drippings from baking sheet, vinegar and remaining 3 tablespoons sugar to skillet used to brown hens. Bring to boil, scraping up any browned bits. Add stock and bring to boil. Mix remaining 4 tablespoons butter and flour in small bowl, forming paste. Whisk paste into stock mixture. Boil until thickened to sauce consistency, about 3 minutes. Season to taste with salt and pepper. Rewarm onion compote; spoon onto center of each plate. Arrange 2 hen quarters around compote. Spoon sauce over. Sprinkle with chopped parsley and serve.
Preparation Melt 3 tablespoons butter in large nonstick skillet over medium-high heat. Add onions and 3 tablespoons sugar. Cook until onions are golden, stirring often, about 15 minutes. Reduce heat to medium-low. Add wine and cook until onions are very tender and mixture is reduced to thick jamlike consistency, stirring frequently, about 40 minutes. Set compote aside. Preheat oven to 450°F. Melt 2 tablespoons butter in heavy large skillet over medium-high heat. Add hen quarters and brown well on all sides, about 8 minutes. Place hen quarters on rimmed baking sheet (do not clean skillet). Sprinkle hens with salt and pepper. Bake hen quarters until cooked through, about 20 minutes. Transfer hen quarters to bowl; cover to keep warm. Add drippings from baking sheet, vinegar and remaining 3 tablespoons sugar to skillet used to brown hens. Bring to boil, scraping up any browned bits. Add stock and bring to boil. Mix remaining 4 tablespoons butter and flour in small bowl, forming paste. Whisk paste into stock mixture. Boil until thickened to sauce consistency, about 3 minutes. Season to taste with salt and pepper. Rewarm onion compote; spoon onto center of each plate. Arrange 2 hen quarters around compote. Spoon sauce over. Sprinkle with chopped parsley and serve.