Peel potatoes, and cut into uniform cubes (about 1/2" - 3/4").
Put potatoes in a pot of cold water and salt well (1-2 tablespoons).
Bring to boil, and cook until done. It is critical to make sure not to overcook, or else they will turn to mashed potatoes. Start testing with a fork after about 8-10 minutes of boiling, depending on their size.
Drain potatoes in a colander, and salt and pepper generously to taste. Be careful to toss gently so that they don't turn to mush.
Gently toss in 1/2 stick of melted butter.
Place potatoes in shallow casserole dish.
Add freshly-grated cheese on top.
Bake in oven or on covered grill for about 5 minutes. Serve immediately.