Meanwhile, heat the remaining 2 teaspoons oil in the skillet over medium-high heat. Add shallot and cook for 30 seconds. Stir in mushrooms and the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper; cook, stirring occasionally and scraping up any browned bits, until the mushrooms are lightly browned, 3 to 5 minutes. Pour in wine, bring to a boil and cook until nearly evaporated, about 3 minutes. Stir in broth, return to a boil and cook until reduced by a third, 3 to 5 minutes. Remove from heat, add butter and swirl until melted.