Heat 1 inch salted water to boiling. Add potatoes. Heat to boiling; reduce heat. Cover and cook until tender, 30 to 35 minutes. Peel and shred potatoes or cut into 1/4 inch strips.
Heat butter in skillet until melted. Add potatoes, onions, and cheese.
Sprinkle with salt and pepper. Cook uncovered over medium heat, turning frequently, until potatoes start to brown, about 10 minutes, adding 1 to 2 Tblsp. butter to prevent sticking if necessary.
Press potatoes with spatula to form a flat cake; sprinkle with water. Cover and cook over low heat, without stirring, until bottom is golden brown and crusty, about 10 minutes. Place inverted platter over skillet; invert potatoes onto platter.