Peel and dice potatoes.
Preheat a 1 2 inch omelette pan or 3-quart saute pan over medium heat until rim of pan is hot-to-the-touch.
Add oil and butter and wait for about 1 more minute.
Add potatoes and cook, lightly stirring often, until golden brown and almost tender when pierced (15 to 20 minutes).
Meanwhile, in a large bowl, combine sour cream, mustard, and chives; stir until blended.
Remove potatoes from heat and let cool for about 5 minutes.
Then add to sour cream mixture and mix lightly to coat well.
Season to taste with salt and pepper.
(At this point, you may cover and refrigerate for up to 24 hours.) Spread potato mixture evenly in a lightly greased 7- by 10-inch oval au gratin pan or 8-inch-square cake pan.
Bake in a 350°F (175°C) oven until mixture is bubbling and golden brown on top (about 20 minutes: 25 to 35 minutes if refrigerated).
Sprinkle with parsley before serving.