Increase heat to medium-high. Add the remaining 1 tablespoon oil to the pan. Add mushrooms and onion and cook, stirring frequently, until the mushrooms have released their liquid, about 5 minutes. Sprinkle with flour and stir to coat the vegetables, 30 seconds to 1 minute. Pour in broth and wine and cook, stirring and scraping up the browned, until thick enough to coat the back of a spoon, 2 to 4 minutes.