Combine flour, salt, and pepper in a large shallow dish; set aside. Heat a large skillet over medium-high heat until very hot. Dredge chicken in seasoned flour, tapping off excess; set aside. Add oil to skillet. When oil is shimmering, add chicken, and cook until lightly browned, about 3 minutes. Turn over, and cook 3 minutes more. Remove chicken to a plate; set aside and keep warm.

Heat 2 tablespoons butter in same skillet. Add mushrooms, and cook, stirring occasionally, until mushrooms are golden brown and all the released liquid has evaporated, 5 to 7 minutes.

Remove skillet from heat, and add wine and broth. Return skillet to heat, scraping up any brown bits with a wooden spoon. Add garlic, lemon juice, remaining 2 tablespoons butter, and parsley. Cook for 2 minutes until reduced and slightly thickened. Taste and adjust for seasoning. Pour sauce over chicken and sprinkle with parsley. Serve immediately.