Cook potatoes in large pot of boiling salted water until tender, about 20 minutes. Drain. (Can be made 2 hours ahead. Let stand at room temperature.)
Melt butter in heavy large skillet over medium-high heat. Add potatoes, 4 tablespoons parsley, lemon peel, lemon juice, salt, and pepper. Cook until potatoes are heated through and beginning to brown, tossing often, about 5 minutes.
Transfer to bowl. Sprinkle with 2 tablespoons parsley and serve.