Combine apples, mayo and walnuts. Place a slice of cheese on four slices of bread. Layer each with 1/3 c of the apple mix, a slice of ham and another slice of cheese. Cover with remaining bread. Butter the outsides of the sandwiches. Cook in a large skillet over medium heat on each side until bread is golden and cheese is melted.
Lower the fat and calories by using reduced-fat cheese, reduced-fat mayo, and omit butter on the bread.