Peel the potatoes, cut them into halves. Make 1/8 (3 mm) cuts on each, not all the way through.
Smear a tray with oil and arrange the potatoes in it, sprinkle with salt, paprika and black pepper to taste. Cut the butter into small cubes and distribute them evenly over the potatoes.
Place tray in preheated 392°F (200 °C) oven and bake 20-25 min. to golden-brown crisp.
Shortly before they're ready, sprinkle with the grated cheese and leave in the oven until the cheese melts.