Heat 1 tablespoon oil in large nonstick skillet over medium-low heat. Add onion and garlic and saute until tender, about 5 minutes. Add mushrooms, thyme and lemon peel to skillet and stir. Cover and cook until mushrooms are tender, about 5 minutes. Uncover, increase heat to high and cook until mushrooms begin to brown, about 6 minutes.
Cool slightly. Transfer mushroom mixture to processor. Add cheese, lemon juice, remaining half tablespoon oil and finely chop, using on/off turns.
Mix in parsley; season with salt and pepper. Transfer to small bowl.
Notes: Can be made 3 hours ahead. Let stand at room temperature. Serve with toasted bread rounds. Makes about 1- half cups.