Heat 1 tablespoon oil in a large nonstick skillet over medium heat. Add onion and cook until softened, about 3 minutes. Add mushrooms and cook, stirring, until they release their juices, 10 to 12 minutes.dd garlic and thyme and stir until fragrant, about 30 seconds. Add sherry and cook until mostly evaporated, about 3 minutes. Stir in the remaining 1 tablespoon oil, lemon juice, salt and pepper and continue cooking for 1 minute more. Pour over greens in a large bowl and toss to coat. Sprinkle with Parmesan.