The secret, as with so many things in life, is duck fat. While you could use vegetable oil or another fat with a high smoke point, none of them add the flavour or pretension that comes with duck fat. I make a lot of duck so I've always got mason jars and cereal bowls full of the stuff (honestly, it's kind of gross), but you can also buy it if you don't have any already saved.
The other key is to use a starchy potato, but not too starchy. Russets, aka baking potatoes, are too starchy. Blue potatoes, aka boiling potatoes, are too waxy. I use Yukon gold potatoes but frankly, you can just look at the label on the bag or in the store and if it says "good for roasting" or words to that effect then you should be good to go!
1 potato per person, peeled and halved
1 tablespoon duck fat per potato
1 can beef or chicken stock
Heat duck fat in the oven at ~400 in a roasting pan. While fat is heating, put the potatoes into cool water to cover, add stock and bring to a boil. Cook until potatoes are par-boiled where the outsides start to become soft but the insides are still hard. The stock will impart a bit more flavour if desired and can be left out if desired.
When potatoes are soft on the outside, drain the liquid, put the lid on the pot and shake it like a Polaroid picture* until the outsides of the potatoes get all roughed up. This will make them extra crispy and helps to burn off the carbs you're about to consume.
Add the potatoes to the fat, tossing to coat and put in oven for 30-40 minutes rolling around once in the middle.
Let cool for ~5 minutes and then serve. Goes well with just about anything (I'd put them on my cereal if it were social acceptable).
* Polaroid does not endorse the shaking of their film to aid the development process. Doing so may result in smeared or blurred pictures but is one hell of a dance move.