Cook potatoes in boiling water to cover 30 minutes or until tender; drain well. Return potatoes to pan. Add butter, and mash with a potato masher. Add half-and-half, salt, and pepper. Mash again to desired consistency.
Sauté green onions in hot oil in a medium skillet over medium-high heat 5 minutes or until crisp-tender. Add onions and walnuts to mashed potato, stirring until blended.
Note: Chop walnuts by hand for this recipe instead of using a processor because a processor often creates "dust" that can discolor the potatoes.