Grate the potatoes on a large cheese grater and season with salt and pepper.
Heat a little olive oil in a non-stick frying pan. For each galette, place a large spoonful of grated potato in the pan and flatten out with a spatula so that a lacey effect is created. Fry until crisp on one side, then turn over and fry the other side. Dry the galettes on absorbent kitchen paper. Keep warm.
To serve with the medaglioni.