Preheat a 12-in. omelette pan or 3-qt. sauté pan over medium heat until rim 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, about 15 - 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.
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.)
Preheat oven to 350°F/180°C.
Spread potato mixture evenly in a lightly-greased oval au gratin pan or 8-in. square cake can.
Bake in oven until mixture is bubbling and golden brown on top, about 20 minutes.
Sprinkle with parsley before serving.