In a 3-quart saucepan heat oil over medium heat. Add onion; cook 5 minutes. Add broth, pepper, and salt to taste. Bring to boiling. Add potatoes and return to boiling; reduce heat. Simmer, covered, 10 minutes.
Meanwhile, in large skillet melt butter over medium heat. Add mushrooms; cook 6 to 8 minutes or until tender and liquid has evaporated. Set mushrooms aside.
Remove saucepan from heat. Using an immersion blender, blend onion-potato mixture until almost smooth. Add spinach, arugula, and parsley. Return to heat. Bring to boiling; remove from heat. Using immersion blender, puree soup again until nearly smooth and flecks of green remain. Top servings with sauteed mushrooms and, if desired, additional arugula.