Preheat oven to 425 degrees. Pat chicken quarters dry and place on a sheet pan skin side up. Rub top of each chicken piece with olive oil. Liberally season with salt and pepper then bake 35 minutes. Meanwhile in a large skillet, melt 2 tbsp butter with olive oil over medium heat. Add onion and green onion then saute 5 minutes. Add mushrooms and continue to saute an additional 10 minutes. Add garlic and continue to saute 1 minute. Add remaining butter. Once butter has melted, add flour and cook 2 minutes, stirring constantly. Lower heat to low and add wine to deglaze the pan. Once deglazed, return heat to medium high, and add chicken stock, parsley and rosemary then continue to cook, stirring often. Once sauce has reached desired thickness, reduce heat to low and stir occasionally. When chicken has finished cooking, let rest under foil for 10 minutes. Serve chicken with a spoonful of sauce over each piece.