Heat oven to 350°F. Spray 13x9-inch (3-quart) glass baking dish with nonstick cooking spray. Place spreadable cheese in medium bowl. Gradually stir in half-and-half and chiles; blend well. Set aside.
In sprayed baking dish, layer potatoes, broccoli and ham. Pour spreadable cheese mixture over top; sprinkle with Cheddar cheese. Cover with foil.
Bake at 350°F. for 45 minutes. Uncover; bake an additional 15 minutes or until bubbly around edges.