For marinade, in a small bowl combine onion, wine, lime juice, oil, savory, salt, and hot pepper sauce. Set aside.
Place pheasant in a large resealable plastic bag set in a bowl. Pour marinade over pheasant. Seal bag; turn pheasant to coat well. Marinate in the refrigerator for 6 to 24 hours, turning bag occasionally. Remove pheasant from bag, reserving marinade.
Tie legs to tail. Twist wing tips under back (see photo 4). Place pheasant, breast side up, on a rack in a shallow roasting pan. Cover pheasant with foil, leaving air space between bird and foil. Lightly press the foil to the ends of drumsticks and neck to enclose bird. Roast in a 350 degrees F oven for 75 to 90 minutes. After about 60 minutes of roasting, remove foil and cut string between drumsticks. Continue roasting until drumsticks move easily in their sockets and juices run clear (180 degrees F). (Check temperature of thigh in several places with a meat thermometer.)
Meanwhile, strain marinade, reserving 1/2 cup. In a medium saucepan melt butter over medium heat; stir in flour. Add the reserved 1/2 cup marinade and the chicken broth. Cook and stir until thickened and bubbly; cook and stir for 1 minute more. Stir in parsley. Season to taste with black pepper. Makes 4 servings.