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