Melt the butter with the oil in a large frying pan. As soon as the butter stops foaming, add the mushrooms, garlic, thyme, lemon rind and salt and pepper and cook over a medium heat, stirring, for 4–5 minutes until tender. Scatter over the parsley and squeeze over a little lemon juice.
Meanwhile, toast the bread, then arrange it on serving plates.
Top the sourdough toast with an equal quantity of the salad leaves and mushrooms, and drizzle over a little more oil and lemon juice. Scatter with Parmesan shavings and serve immediately.