Heat 1 inch water to boiling in 2-quart saucepan. Add potatoes. Cover and heat to boiling; reduce heat to medium-low. Cover and cook 6 to 8 minutes or until potatoes are tender; drain.

Beat eggs, milk, salt and pepper with fork or wire whisk until a uniform yellow color; set aside.

In a large skillet, melt butter and add potatoes, and sausage to skillet. Cook for about 3 to 5 minutes, turning potatoes occasionally, until light brown. Stir in green onions. Cook 1 minute, stirring constantly.

Pour egg mixture into skillet. As mixture begins to set at bottom and side, gently lift cooked portions with spatula so that thin, uncooked portion can flow to bottom. Avoid constant stirring. Cook 3 to 4 minutes or until eggs are thickened throughout but still moist. Sprinkle with cheese. Serves 6.