Place potatoes in a large saucepan and cover with water. Bring to a boil. Reduce heat; cover and cook for 15-20 minutes or until tender. Drain and mash.
In a small bowl, whisk the egg yolks, milk, salt, basil and pepper. Gradually stir into mashed potatoes. Fold in 1 cup cheese. In a small bowl, beat egg whites on high speed until stiff peaks form; fold into potato mixture.
Spoon into a greased 1-1/2-qt. baking dish. Sprinkle with remaining cheese. Bake, uncovered, at 350° for 40-45 minutes or until a thermometer reads 160°.