Cook the potatoes whole in a large pot of boiling salted water until tender (about 20 minutes, don't overcook them, only JUST until fork-tender).

Drain and cool slightly (this can be done up to 2 hours in advance and kept at room temperature).

In a large heavy skillet over medium heat, melt the butter.

Add in cooked potatoes with about 1/4 cup fresh chopped parsley, lemon peel, lemon juice, salt and pepper.

Cook until potatoes are beginning to brown, tossing them often (about 5-6 minutes).

Transfer to a large serving bowl.

Sprinkle with about 2-3 tablespoons more of fresh parsley.