Heat 1/4 cup of the oil in a medium skillet over high heat. When the oil is hot, add the mushrooms and sauté, stirring occasionally, for 3 minutes. Remove from the heat.
Turn the mushrooms and oil into a food processor or blender, add the egg and purée for 30 seconds. Add the sherry, shallots, garlic, Parmesan, lemon juice, salt, and pepper and purée for 15 seconds. With the machine running, stream in the remaining 1/4 cup oil and process until thoroughly blended. Serve immediately.
Yield: 1 cup