Heat 2 tablespoons butter and the oil in a large skillet over medium-high heat until butter is melted.
Meanwhile, coat chicken in flour; shake off excess. Working in batches if necessary to avoid crowding skillet, add chicken to skillet; sauté chicken over medium-high heat 4 to 6 minutes or until golden brown, turning once. Remove chicken from skillet.
Add the mushrooms; sauté 2 minutes or until browned. Add the wine, 1/4 cup beef broth and the salt to skillet; simmer for 2 minutes, scraping up any bits from bottom of skillet with a wooden spoon.
Return chicken to skillet. Bring to a boil over high heat. Cover and reduce heat to low; simmer for 15 to 20 minutes or until cooked through, basting occasionally.
Remove chicken to serving platter and keep warm. Add the remaining beef broth to skillet. Bring to a boil; boil for 2 minutes. Remove skillet from from heat. Stir in remaining 2 tablespoons butter until just incorporated.
To serve, pour sauce over chicken and sprinkle with parsley.