Heat the oven to 180°C/160°C Fan/350°F. Get out a smallish roasting tin that can go on the stove, and sear the duck legs, skin-side down over medium heat, until the skin turns golden and gives out some oil. Keep an eye on the duck while you cut the potatoes into approx. 3cm / 1½-inch cubes. I don't peel them.
Turn the legs over, preferably using a thin spatula, and taking care to dislodge the legs without ripping the skin. If the legs are very stuck on, it means they haven't crisped up enough yet.
Arrange your potatoes around the duck legs, then let a few sprigs of thyme fall over the duck and potatoes, and sprinkle with salt and pepper, before putting into the oven.
Cook for 2 hours, for optimal outcome, which is crisp-skinned and tender-fleshed duck and potatoes that are crunchy on the outside and divinely soaked through with duck fat on the inside, though both should be ready to eat after 1½ hours. I used to turn the potatoes over while cooking this, but have decided it is not necessary and, indeed, not desirable.