Heat oil in a large frying pan. Add mochi and cook, covered, over low heat until mochi bottoms are slightly browned (about 5 minutes). Flip mochi pieces, add 1 - 2 teaspoons water to create steam and to soften mochi, cover again, and cook a few minutes more. Remove cover as soon as mochi is cooked (to prevent mochi from melting).
Cooked mochi is often served with a shoyu and ginger-based dip. It can also be rolled in a mixture of equal parts shoyu and water, then wrapped in strips of toasted nori.