Fill a large pot with at least 2 quarts of water and 2 teaspoons salt. Place the potatoes in the water and bring it up to a boil. Cook until fork tender, about 25 minutes. Drain the potatoes and set aside to cool. Peel once you are able to handle them with your hands.

Chop the potatoes into ½ inch cubes and spread over a large, parchment lined baking sheet. Refrigerate until cold, about 15 minutes.

Heat about ½ cup oil in a wide frying pan over medium heat. Check the oil heat by dropping a piece of potato into it. If it bubbles immediately, it is ready. Add the cold potatoes to the hot oil in a single layer, leaving to fry, undisturbed for 5, until crispy and browned (you may have to complete this step in multiple batches). Flip and fry for another 5 minutes. Flip once again, frying another 3-5 minutes, until they’re golden and crispy. Remove the potatoes from the pan and place on a paper towel lined baking sheet. Evenly sprinkle with w 1 ½ teaspoons salt, carefully turning the potatoes as you go.

Remove the potatoes from the heat and transfer to a paper towel lined plate. Sprinkle the potatoes with ¾ teaspoon salt. Drain the oil from the pan and return the potatoes to the pan. 

Grate the gruyere on a box grater and toss it with the hot potatoes over low heat until melted. Serve hot with freshly ground black pepper.