Cut the potatoes into ¾-inch (2-cm) pieces and cook in boiling salted water until tender, about 15 minutes. Drain potatoes, reserving about ½ cup (4 fl oz/125 ml) of the cooking liquid, and return to the hot pot. Using a fork, mash the potatoes coarsely, thinning them to the desired consistency with the reserved cooking liquid. Stir in the butter or olive oil and season to taste with salt and pepper. Serve right away.