Preheat oven to 375 degrees.
Melt butter or margarine in an oven-safe skillet (e.g., cast iron). Add potatoes; cook until soft and browned, stirring occasionally.
Meanwhile, in medium bowl or 2-cup measure beat eggs and milk with a fork. Stir in cheese.
When potatoes soft and browned, season to taste. Add ham and toss to evenly combine with potatoes in skillet. Use pancake turner to press the potato mixture into an even layer.
Stir egg mixture and pour evenly over potatoes. Keep on burner until egg mixture begins to set around outside edge. Place skillet in oven and bake 20- 25 minutes or till no longer jiggly.
Cut into 4 wedges to serve.